Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20276972 | C2 | semidirect |
| 2. #20276971 | C2 | semidirect |
| 3. #20276970 | C2 | semidirect |
| 4. #20274331 | C2 | semidirect |
| 6. C16×#88322 | C2 | semidirect |
| 7. C53×#2248 | C2 | semidirect |
| 64. C16×C53 | D8 | semidirect |
| 65. #11719908 | D8 | semidirect |
| 84. #88322 | SD32 | semidirect |
| 99. #2248 | D53 | semidirect |
| 120. C53 | #12517 | semidirect |
| 165. C16 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276972 | 2 |
| #20276971 | 2 |
| #20276970 | 2 |
| #20274331 | 2 |
| #20274329 | 2 |
| C16×#88322 | 2 |
| C53×#2248 | 2 |
| #12517 | 53 |