Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 134 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 | C89×#2535 | C2 |
| 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×#2975 | C2 | semidirect |
| 3. C89×#1800 | C2 | semidirect |
| 4. C89×#1486 | C2 | semidirect |
| 5. C89×#1286 | C2 | semidirect |
| 47. C4×C8×C89 | D4 | semidirect |
| 156. #9489 | C89 | direct (N × H) |
| 164. #2975 | C2×C89 | semidirect |
| 166. #1800 | C2×C89 | semidirect |
| 167. #1486 | C2×C89 | semidirect |
| 168. #1286 | C2×C89 | semidirect |
| 169. C89 | #9489 | direct (N × H) |
| 211. 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×#2975 | 2 |
| C89×#2535 | 2 |
| C89×#1800 | 2 |
| C89×#1486 | 2 |
| C89×#1286 | 2 |
| #9489 | 89 |