Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 122 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. #20290921 | C2 | semidirect |
| 2. C2×#16811486 | C2 | semidirect |
| 3. #20289671 | C2 | semidirect |
| 4. #20289669 | C2 | semidirect |
| 52. #135×C53 | C8 | semidirect |
| 71. Q16×C53 | C2×C8 | semidirect |
| 74. D8×C53 | C2×C8 | semidirect |
| 174. C53 | #11592 | semidirect |
| 177. #135 | #88324 | semidirect |
| 221. Q16 | C2×#88324 | semidirect |
| 224. D8 | C2×#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290921 | 2 |
| C2×#16811486 | 2 |
| #20289671 | 2 |
| #20289669 | 2 |
| #135×Dic53 | 2 |
| #11592 | 53 |