Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20280363 | C2 | semidirect |
| 4. #20272608 | C2 | semidirect |
| 5. #20272581 | C2 | semidirect |
| 6. #20272572 | C2 | semidirect |
| 52. C4⋊Q8×C53 | Q8 | semidirect |
| 53. #127×C53 | Q8 | semidirect |
| 208. C53 | #10378 | semidirect |
| 212. C4⋊Q8 | Dic106 | semidirect |
| 213. #127 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280363 | 2 |
| #20275635 | 2 |
| #20273262 | 2 |
| #20272608 | 2 |
| #20272581 | 2 |
| #20272572 | 2 |
| C53×#1505 | 2 |
| #10378 | 53 |