Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#15667955 | C2 | semidirect |
| 2. C2×#19151870 | C2 | semidirect |
| 4. C2×#19151412 | C2 | semidirect |
| 5. C2×#19151383 | C2 | semidirect |
| 6. #26018347 | C2 | semidirect |
| 7. C89×#2141 | C2 | semidirect |
| 56. C2×#13083549 | D4 | semidirect |
| 58. #15667948 | D4 | semidirect |
| 67. C2×Q16×C89 | D4 | semidirect |
| 199. #2141 | D89 | semidirect |
| 202. C89 | #13321 | semidirect |
| 235. C2×Q16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667955 | 2 |
| C2×#19151870 | 2 |
| #26029901 | 2 |
| C2×#19151412 | 2 |
| C2×#19151383 | 2 |
| #26018347 | 2 |
| C89×#2141 | 2 |
| #13321 | 89 |