Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
654 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20283624 | C2 | semidirect |
| 2. #20283358 | C2 | semidirect |
| 3. #20276267 | C2 | semidirect |
| 4. #20276021 | C2 | semidirect |
| 6. #20275417 | C2 | semidirect |
| 7. #20275217 | C2 | semidirect |
| 8. #20275078 | C2 | semidirect |
| 9. #20275002 | C2 | semidirect |
| 10. #20274865 | C2 | semidirect |
| 11. C53×#2103 | C2 | semidirect |
| 188. #2103 | D53 | semidirect |
| 229. C53 | #29386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283624 | 2 |
| #20283358 | 2 |
| #20276267 | 2 |
| #20276021 | 2 |
| #20275820 | 2 |
| #20275417 | 2 |
| #20275217 | 2 |
| #20275078 | 2 |
| #20275002 | 2 |
| #20274865 | 2 |
| C53×#2103 | 2 |
| #29386 | 53 |