Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20287671 | C2 | semidirect |
| 2. #20276956 | C2 | semidirect |
| 3. #20274196 | C2 | semidirect |
| 4. #20272766 | C2 | semidirect |
| 5. #20272696 | C2 | semidirect |
| 6. #20272682 | C2 | semidirect |
| 74. D8×C53 | SD16 | semidirect |
| 172. C53 | #12360 | semidirect |
| 221. D8 | #11719923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287671 | 2 |
| #20276956 | 2 |
| #20274196 | 2 |
| #20272766 | 2 |
| #20272696 | 2 |
| #20272682 | 2 |
| C53×#2206 | 2 |
| #12360 | 53 |