Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
576 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 576 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. #20277872 | C2 | semidirect |
| 2. #20275552 | C2 | semidirect |
| 3. #20273244 | C2 | semidirect |
| 4. #20273231 | C2 | semidirect |
| 5. #20272622 | C2 | semidirect |
| 6. #20272569 | C2 | semidirect |
| 26. C53×#481 | C4 | semidirect |
| 29. C53×#447 | C4 | semidirect |
| 57. C22×D4×C53 | C2×C4 | semidirect |
| 70. C2×C4⋊C4×C53 | C2×C4 | semidirect |
| 78. C22⋊C8×C53 | C2×C4 | semidirect |
| 259. #481 | Dic53 | semidirect |
| 262. #447 | Dic53 | semidirect |
| 279. C53 | #9343 | semidirect |
| 282. C22×D4 | C2×Dic53 | semidirect |
| 299. C2×C4⋊C4 | C2×Dic53 | semidirect |
| 320. C22⋊C8 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277872 | 2 |
| #20275552 | 2 |
| #20273244 | 2 |
| #20273231 | 2 |
| #20272622 | 2 |
| #20272569 | 2 |
| C53×#3192 | 2 |
| #9343 | 53 |