Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20285243 | C2 | semidirect |
| 4. #20272822 | C2 | semidirect |
| 5. #20272817 | C2 | semidirect |
| 6. #20272802 | C2 | semidirect |
| 53. C2×Q16×C53 | Q8 | semidirect |
| 55. C2×D8×C53 | Q8 | semidirect |
| 181. C53 | #13374 | semidirect |
| 187. C2×Q16 | Dic106 | semidirect |
| 189. C2×D8 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285243 | 2 |
| #20276451 | 2 |
| #20275614 | 2 |
| #20272822 | 2 |
| #20272817 | 2 |
| #20272802 | 2 |
| C2×C53×#360 | 2 |
| #13374 | 53 |