Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
448 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 76 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. D53⋊#349 | C2 | semidirect |
| 2. #20290387 | C2 | semidirect |
| 3. #20289688 | C2 | semidirect |
| 4. #20289685 | C2 | semidirect |
| 12. C2×#13133236 | C4 | semidirect |
| 16. #16810881 | C4 | semidirect |
| 20. #16810658 | C4 | semidirect |
| 22. C53×#469 | C4 | semidirect |
| 37. C2×Dic212 | C2×C4 | semidirect |
| 55. #13133149 | C2×C4 | semidirect |
| 59. C2×D8×C53 | C2×C4 | semidirect |
| 62. #106×C53 | C2×C4 | semidirect |
| 206. #469 | #6157 | semidirect |
| 215. C53 | #11685 | semidirect |
| 222. C2×D8 | C2×#6157 | semidirect |
| 252. #106 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#349 | 2 |
| #20290387 | 2 |
| #20289688 | 2 |
| #20289685 | 2 |
| #20284322 | 2 |
| #11685 | 53 |