Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
778 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 224 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 |
|---|---|---|
| 2. #20289535 | C2 | direct (N × H) |
| 33. C22×Q8×C53 | C8 | semidirect |
| 46. C2×Q8×C53 | C2×C8 | semidirect |
| 132. C2×C53 | #1272 | semidirect |
| 148. C53 | C2×#1272 | semidirect |
| 153. C22×Q8 | #88324 | semidirect |
| 181. C2×Q8 | C2×#88324 | semidirect |
| 263. C2 | #20289535 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811489 | 2 |
| #20289535 | 2 |
| C2×#16810530 | 2 |
| C2×#1272 | 53 |