Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
330 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20276971 | C2 | semidirect |
| 2. #20276968 | C2 | semidirect |
| 4. #20274321 | C2 | semidirect |
| 5. C8×C16×C53 | C2 | semidirect |
| 67. C8×C16 | D53 | semidirect |
| 80. C53 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276971 | 2 |
| #20276968 | 2 |
| #20276965 | 2 |
| #20274321 | 2 |
| C8×C16×C53 | 2 |
| #12518 | 53 |