Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
364 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 364 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 | C4×C13 | C2×D8 |
| commutator, Frattini, cosocle | C8 | C24×C13 |
| socle | C2×C13 | C22×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C22×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#135 | C2 | semidirect |
| 2. C13×#510 | C2 | semidirect |
| 3. C13×#509 | C2 | semidirect |
| 4. C13×#508 | C2 | semidirect |
| 5. C2×C13×M32 | C2 | semidirect |
| 10. C13×#135 | C22 | semidirect |
| 11. C2×C13×Q16 | C22 | semidirect |
| 13. C2×C13×D8 | C22 | semidirect |
| 15. C13×Q32 | C22 | semidirect |
| 16. C13×SD32 | C22 | semidirect |
| 17. C13×D16 | C22 | semidirect |
| 18. C13×M32 | C22 | semidirect |
| 19. C2×C13×C16 | C22 | semidirect |
| 40. #3414 | C13 | direct (N × H) |
| 59. C2×#135 | C2×C13 | semidirect |
| 60. #510 | C2×C13 | semidirect |
| 61. #509 | C2×C13 | semidirect |
| 62. #508 | C2×C13 | semidirect |
| 63. C2×M32 | C2×C13 | semidirect |
| 77. #135 | C22×C13 | semidirect |
| 78. C2×Q16 | C22×C13 | semidirect |
| 80. C2×D8 | C22×C13 | semidirect |
| 82. Q32 | C22×C13 | semidirect |
| 83. SD32 | C22×C13 | semidirect |
| 84. D16 | C22×C13 | semidirect |
| 85. M32 | C22×C13 | semidirect |
| 86. C2×C16 | C22×C13 | semidirect |
| 111. C13 | #3414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#135 | 2 |
| C13×#510 | 2 |
| C13×#509 | 2 |
| C13×#508 | 2 |
| C2×C13×M32 | 2 |
| #3414 | 13 |