Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
734 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 734 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. C2×#16811466 | C2 | semidirect |
| 2. #20289641 | C2 | semidirect |
| 3. #20289639 | C2 | semidirect |
| 41. C22×D4×C53 | C8 | semidirect |
| 54. C24×C53 | C2×C8 | semidirect |
| 69. C22×C4×C53 | C2×C8 | semidirect |
| 199. C53 | #11426 | semidirect |
| 207. C22×D4 | #88324 | semidirect |
| 235. C24 | C2×#88324 | semidirect |
| 261. C22×C4 | C2×#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811466 | 2 |
| #20289641 | 2 |
| #20289639 | 2 |
| #20277293 | 2 |
| #11426 | 53 |