Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
988 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26031010 | C2 | semidirect |
| 2. #26028539 | C2 | semidirect |
| 4. #26018825 | C2 | semidirect |
| 5. #26018821 | C2 | semidirect |
| 6. #26018120 | C2 | semidirect |
| 7. C89×#1779 | C2 | semidirect |
| 33. C22×Dic178 | D4 | semidirect |
| 53. C2×C4⋊Dic89 | D4 | semidirect |
| 70. #15667919 | D4 | semidirect |
| 82. C22×C8×C89 | D4 | semidirect |
| 139. C24×C89 | SD16 | semidirect |
| 316. #1779 | D89 | semidirect |
| 320. C89 | #10322 | semidirect |
| 362. C22×C8 | C22⋊D89 | semidirect |
| 410. C24 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| #26028539 | 2 |
| #26028534 | 2 |
| #26018825 | 2 |
| #26018821 | 2 |
| #26018120 | 2 |
| C89×#1779 | 2 |
| #10322 | 89 |