Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
532 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 8. #19151340 | C4 | direct (N × H) |
| 92. C4×C89 | #330 | semidirect |
| 103. C89 | C4×#330 | semidirect |
| 191. C4 | #19151340 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667923 | 2 |
| C2×#19151340 | 2 |
| #26018133 | 2 |
| C4×#125×C89 | 2 |
| C4×#330 | 89 |