Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 446 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. #20280887 | C2 | semidirect |
| 4. #20272622 | C2 | semidirect |
| 5. #20272600 | C2 | semidirect |
| 6. #20272567 | C2 | semidirect |
| 52. C22×D4×C53 | Q8 | semidirect |
| 59. C2×C4⋊C4×C53 | Q8 | semidirect |
| 236. C53 | #10382 | semidirect |
| 239. C22×D4 | Dic106 | semidirect |
| 251. C2×C4⋊C4 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280887 | 2 |
| #20275552 | 2 |
| #20273231 | 2 |
| #20272622 | 2 |
| #20272600 | 2 |
| #20272567 | 2 |
| C53×#1510 | 2 |
| #10382 | 53 |