Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20283854 | C2 | semidirect |
| 2. #20275643 | C2 | semidirect |
| 3. #20273429 | C2 | semidirect |
| 4. #20273240 | C2 | semidirect |
| 5. #20272584 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 26. C53×#496 | C4 | semidirect |
| 27. C53×#490 | C4 | semidirect |
| 225. #496 | Dic53 | semidirect |
| 226. #490 | Dic53 | semidirect |
| 248. C53 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283854 | 2 |
| #20275643 | 2 |
| #20273429 | 2 |
| #20273240 | 2 |
| #20272584 | 2 |
| #20272570 | 2 |
| C53×#3217 | 2 |
| #9378 | 53 |