Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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. #20289757 | C2 | semidirect |
| 2. #20289555 | C2 | semidirect |
| 29. C2×Q16×C53 | C8 | semidirect |
| 31. C2×D8×C53 | C8 | semidirect |
| 117. C53 | #7109 | semidirect |
| 121. C2×Q16 | #88324 | semidirect |
| 123. C2×D8 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289757 | 2 |
| #20289555 | 2 |
| #20275609 | 2 |
| #7109 | 53 |