Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20276940 | C2 | semidirect |
| 2. #20276939 | C2 | semidirect |
| 3. #20276938 | C2 | semidirect |
| 4. #20274332 | C2 | semidirect |
| 6. C16×#88322 | C2 | semidirect |
| 7. C53×#2240 | C2 | semidirect |
| 108. #2240 | D53 | semidirect |
| 132. C53 | #12509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276940 | 2 |
| #20276939 | 2 |
| #20276938 | 2 |
| #20274332 | 2 |
| #20274329 | 2 |
| C16×#88322 | 2 |
| C53×#2240 | 2 |
| #12509 | 53 |