Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 106 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. #20290266 | C2 | semidirect |
| 4. M16×#88324 | C2 | semidirect |
| 5. #20289561 | C2 | semidirect |
| 6. #20289548 | C2 | semidirect |
| 59. #100×C53 | C8 | semidirect |
| 194. C53 | #9550 | semidirect |
| 216. #100 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290266 | 2 |
| #20290014 | 2 |
| C2×D4⋊#88324 | 2 |
| M16×#88324 | 2 |
| #20289561 | 2 |
| #20289548 | 2 |
| #100×Dic53 | 2 |
| #9550 | 53 |