Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
236 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20276546 | C2 | semidirect |
| 3. #20272669 | C2 | semidirect |
| 4. #20272633 | C2 | semidirect |
| 5. C53×#1367 | C2 | semidirect |
| 59. C8×C53 | M32 | semidirect |
| 75. #1367 | D53 | semidirect |
| 92. C53 | #12064 | semidirect |
| 137. C8 | #13133156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276546 | 2 |
| C8×D424 | 2 |
| #20272669 | 2 |
| #20272633 | 2 |
| C53×#1367 | 2 |
| #12064 | 53 |