Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20276750 | C2 | semidirect |
| 2. #20274329 | C2 | semidirect |
| 3. D8×#88322 | C2 | semidirect |
| 4. #20272784 | C2 | semidirect |
| 5. #20272762 | C2 | semidirect |
| 6. #20272761 | C2 | semidirect |
| 7. C53×#2206 | C2 | semidirect |
| 58. D8×C53 | D8 | semidirect |
| 104. #88322 | D16 | semidirect |
| 123. #2206 | D53 | semidirect |
| 150. C53 | #12424 | semidirect |
| 192. D8 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276750 | 2 |
| #20274329 | 2 |
| D8×#88322 | 2 |
| #20272784 | 2 |
| #20272762 | 2 |
| #20272761 | 2 |
| C53×#2206 | 2 |
| #12424 | 53 |