Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
502 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20276297 | C2 | semidirect |
| 2. #20276268 | C2 | semidirect |
| 3. #20276175 | C2 | semidirect |
| 4. #20276113 | C2 | semidirect |
| 5. #20275985 | C2 | semidirect |
| 6. #20275968 | C2 | semidirect |
| 7. #20275197 | C2 | semidirect |
| 8. #20274934 | C2 | semidirect |
| 176. C53 | #32870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276297 | 2 |
| #20276268 | 2 |
| #20276175 | 2 |
| #20276113 | 2 |
| #20275985 | 2 |
| #20275968 | 2 |
| #20275197 | 2 |
| #20274934 | 2 |
| C53×#2018 | 2 |
| #32870 | 53 |