Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
686 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20284715 | C2 | semidirect |
| 2. #20284179 | C2 | semidirect |
| 3. #20273274 | C2 | semidirect |
| 4. #20273140 | C2 | semidirect |
| 5. #20273106 | C2 | semidirect |
| 6. #20272573 | C2 | semidirect |
| 7. C53×#2535 | C2 | semidirect |
| 40. #13133217 | D4 | semidirect |
| 41. #13133214 | D4 | semidirect |
| 51. C4⋊#88322 | D4 | semidirect |
| 59. C4×#88322 | D4 | semidirect |
| 99. C2×D4×C53 | D8 | semidirect |
| 251. #2535 | D53 | semidirect |
| 289. C53 | #9996 | semidirect |
| 365. C2×D4 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284715 | 2 |
| #20284179 | 2 |
| #20273274 | 2 |
| #20273140 | 2 |
| #20273106 | 2 |
| #20272573 | 2 |
| C53×#2535 | 2 |
| #9996 | 53 |