Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
360 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C24×C11 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C11×#41 ◁ C11×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#578 | C2 | semidirect |
| 2. C11×#576 | C2 | semidirect |
| 3. C11×#510 | C2 | semidirect |
| 4. C11×#509 | C2 | semidirect |
| 5. C11×#508 | C2 | semidirect |
| 6. C2×C11×SD32 | C2 | semidirect |
| 7. C11×#504 | C2 | semidirect |
| 13. C11×#135 | C22 | semidirect |
| 14. C2×C11×Q16 | C22 | semidirect |
| 17. C11×Q32 | C22 | semidirect |
| 18. C11×SD32 | C22 | semidirect |
| 19. C11×SD32 | C22 | semidirect |
| 20. C11×SD32 | C22 | semidirect |
| 21. C11×D16 | C22 | semidirect |
| 22. C11×M32 | C22 | semidirect |
| 23. C2×C11×C16 | C22 | semidirect |
| 45. #3416 | C11 | direct (N × H) |
| 63. #578 | C2×C11 | semidirect |
| 64. #576 | C2×C11 | semidirect |
| 65. #510 | C2×C11 | semidirect |
| 66. #509 | C2×C11 | semidirect |
| 67. #508 | C2×C11 | semidirect |
| 68. C2×SD32 | C2×C11 | semidirect |
| 69. #504 | C2×C11 | semidirect |
| 83. #135 | C22×C11 | semidirect |
| 84. C2×Q16 | C22×C11 | semidirect |
| 87. Q32 | C22×C11 | semidirect |
| 88. SD32 | C22×C11 | semidirect |
| 89. SD32 | C22×C11 | semidirect |
| 90. SD32 | C22×C11 | semidirect |
| 91. D16 | C22×C11 | semidirect |
| 92. M32 | C22×C11 | semidirect |
| 93. C2×C16 | C22×C11 | semidirect |
| 119. C11 | #3416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#578 | 2 |
| C11×#576 | 2 |
| C11×#510 | 2 |
| C11×#509 | 2 |
| C11×#508 | 2 |
| C2×C11×SD32 | 2 |
| C11×#504 | 2 |
| #3416 | 11 |