Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20276527 | C2 | semidirect |
| 2. #20273018 | C2 | semidirect |
| 3. #20272691 | C2 | semidirect |
| 4. #20272688 | C2 | semidirect |
| 7. #16810444 | C22 | semidirect |
| 11. #16810344 | C22 | semidirect |
| 12. C8×#88322 | C22 | semidirect |
| 59. Q16×C53 | M16 | semidirect |
| 63. D8×C53 | M16 | semidirect |
| 146. C53 | #11669 | semidirect |
| 184. Q16 | #11719917 | semidirect |
| 188. D8 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276527 | 2 |
| #20273018 | 2 |
| #20272691 | 2 |
| #20272688 | 2 |
| C53×#2956 | 2 |
| #11669 | 53 |