Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
632 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26030260 | C2 | semidirect |
| 2. #26030049 | C2 | semidirect |
| 3. #26018815 | C2 | semidirect |
| 4. #26018677 | C2 | semidirect |
| 5. #26018643 | C2 | semidirect |
| 6. #26018110 | C2 | semidirect |
| 35. #15668012 | D4 | semidirect |
| 36. #15668012 | D4 | semidirect |
| 49. C4⋊#10623494 | D4 | semidirect |
| 57. C4×#10623494 | D4 | semidirect |
| 113. C2×D4×C89 | SD16 | semidirect |
| 245. C89 | #10000 | semidirect |
| 337. C2×D4 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030260 | 2 |
| #26030049 | 2 |
| #26018815 | 2 |
| #26018677 | 2 |
| #26018643 | 2 |
| #26018110 | 2 |
| C89×#2535 | 2 |
| #10000 | 89 |