Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20283134 | C2 | semidirect |
| 3. #20273314 | C2 | semidirect |
| 4. #20272607 | C2 | semidirect |
| 5. C53×#1464 | C2 | semidirect |
| 44. #13133128 | D4 | semidirect |
| 185. #1464 | D53 | semidirect |
| 213. C53 | #9387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283134 | 2 |
| #20280402 | 2 |
| #20273314 | 2 |
| #20272607 | 2 |
| C53×#1464 | 2 |
| #9387 | 53 |