Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| prime radical | C2×C13×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#533 | C2 | semidirect |
| 3. C13×#490 | C2 | semidirect |
| 4. C13×#486 | C2 | semidirect |
| 5. C13×#418 | C2 | semidirect |
| 6. C4×C13×M16 | C2 | semidirect |
| 10. C13×C4⋊Q8 | C22 | semidirect |
| 14. C13×#125 | C22 | semidirect |
| 19. C13×#102 | C22 | semidirect |
| 20. C13×#97 | C22 | semidirect |
| 21. C4×C8×C13 | C22 | semidirect |
| 42. #3138 | C13 | direct (N × H) |
| 60. #533 | C2×C13 | semidirect |
| 62. #490 | C2×C13 | semidirect |
| 63. #486 | C2×C13 | semidirect |
| 64. #418 | C2×C13 | semidirect |
| 65. C4×M16 | C2×C13 | semidirect |
| 80. C4⋊Q8 | C22×C13 | semidirect |
| 84. #125 | C22×C13 | semidirect |
| 89. #102 | C22×C13 | semidirect |
| 90. #97 | C22×C13 | semidirect |
| 91. C4×C8 | C22×C13 | semidirect |
| 116. C13 | #3138 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| C2×C13×#127 | 2 |
| C13×#490 | 2 |
| C13×#486 | 2 |
| C13×#418 | 2 |
| C4×C13×M16 | 2 |
| #3138 | 13 |