Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #20276257 | C2 | semidirect |
| 3. #20276186 | C2 | semidirect |
| 5. #20272540 | C2 | semidirect |
| 7. C53×#1271 | C2 | semidirect |
| 185. #1271 | D53 | semidirect |
| 214. C53 | #7805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282692 | 2 |
| #20276257 | 2 |
| #20276186 | 2 |
| #20276120 | 2 |
| #20272540 | 2 |
| #20272535 | 2 |
| C53×#1271 | 2 |
| #7805 | 53 |