Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 55. C2×C4⋊C4×C89 | Q8 | semidirect |
| 56. C2×C4⋊C4×C89 | Q8 | semidirect |
| 201. C89 | #10387 | semidirect |
| 232. C2×C4⋊C4 | Dic178 | semidirect |
| 233. C2×C4⋊C4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025913 | 2 |
| #26020351 | 2 |
| #26020329 | 2 |
| #26018161 | 2 |
| #26018106 | 2 |
| #26018105 | 2 |
| C89×#1826 | 2 |
| #10387 | 89 |