Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
696 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20290812 | C2 | semidirect |
| 3. #20290768 | C2 | semidirect |
| 5. #20290647 | C2 | semidirect |
| 6. #20290642 | C2 | semidirect |
| 45. #126×C53 | C8 | semidirect |
| 66. C4⋊C4×C53 | C2×C8 | semidirect |
| 68. C42×C53 | C2×C8 | semidirect |
| 143. C53 | #23375 | semidirect |
| 150. #126 | #88324 | semidirect |
| 186. C4⋊C4 | C2×#88324 | semidirect |
| 194. C42 | C2×#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290812 | 2 |
| #20290784 | 2 |
| #20290768 | 2 |
| #20290658 | 2 |
| #20290647 | 2 |
| #20290642 | 2 |
| #126×Dic53 | 2 |
| #23375 | 53 |