Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20291085 | C2 | semidirect |
| 2. #20289938 | C2 | semidirect |
| 3. #20289679 | C2 | semidirect |
| 4. #20289677 | C2 | semidirect |
| 7. #16811545 | C22 | semidirect |
| 11. #16811464 | C22 | semidirect |
| 12. C8×#88324 | C22 | semidirect |
| 62. Q16×C53 | M16 | semidirect |
| 66. D8×C53 | M16 | semidirect |
| 146. C53 | #11669 | semidirect |
| 184. Q16 | #11719940 | semidirect |
| 188. D8 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291085 | 2 |
| #20289938 | 2 |
| #20289679 | 2 |
| #20289677 | 2 |
| #20283625 | 2 |
| #11669 | 53 |