Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
514 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | #386 |
| commutator | C22×C4 | C22×C4×C89 |
| Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | #392×C89 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89×#2921 | C2 | semidirect |
| 3. C89×#1490 | C2 | semidirect |
| 4. C89×#1464 | C2 | semidirect |
| 5. C89×#1288 | C2 | semidirect |
| 53. C4×C8×C89 | D4 | semidirect |
| 175. #9494 | C89 | direct (N × H) |
| 183. #2921 | C2×C89 | semidirect |
| 185. #1490 | C2×C89 | semidirect |
| 186. #1464 | C2×C89 | semidirect |
| 187. #1288 | C2×C89 | semidirect |
| 188. C89 | #9494 | direct (N × H) |
| 236. C4×C8 | D4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2921 | 2 |
| C89×#2598 | 2 |
| C89×#1490 | 2 |
| C89×#1464 | 2 |
| C89×#1288 | 2 |
| #9494 | 89 |