Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
452 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20287864 | C2 | semidirect |
| 2. #20277034 | C2 | semidirect |
| 3. #20277033 | C2 | semidirect |
| 4. #20277025 | C2 | semidirect |
| 5. #20277024 | C2 | semidirect |
| 6. Q64×D53 | C2 | semidirect |
| 7. #20277008 | C2 | semidirect |
| 8. C2×C53×Q64 | C2 | semidirect |
| 106. C2×Q64 | D53 | semidirect |
| 131. C53 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287864 | 2 |
| #20277034 | 2 |
| #20277033 | 2 |
| #20277025 | 2 |
| #20277024 | 2 |
| Q64×D53 | 2 |
| #20277008 | 2 |
| C2×C53×Q64 | 2 |
| #33984 | 53 |