Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 112 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. #20291075 | C2 | semidirect |
| 2. C4×D53⋊C16 | C2 | semidirect |
| 3. Q8⋊#11719910 | C2 | semidirect |
| 4. #20289666 | C2 | semidirect |
| 57. #11719949 | C16 | semidirect |
| 95. Q8×C53 | C2×C16 | semidirect |
| 107. D212 | C2×C16 | semidirect |
| 169. C53 | #11613 | semidirect |
| 242. Q8 | D53⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291075 | 2 |
| C4×D53⋊C16 | 2 |
| Q8⋊#11719910 | 2 |
| #20289666 | 2 |
| C8×#11719949 | 2 |
| #11613 | 53 |