Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
494 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | C89×#3213 | C2 |
| LCS | G ▷ C2×C42 ▷ 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×#3226 | C2 | semidirect |
| 3. C2×#489×C89 | C2 | semidirect |
| 4. C89×#1558 | C2 | semidirect |
| 5. C89×#1530 | C2 | semidirect |
| 6. C89×#1469 | C2 | semidirect |
| 7. C89×#1302 | C2 | semidirect |
| 176. #10140 | C89 | direct (N × H) |
| 183. #3226 | C2×C89 | semidirect |
| 185. C2×#489 | C2×C89 | semidirect |
| 186. #1558 | C2×C89 | semidirect |
| 187. #1530 | C2×C89 | semidirect |
| 188. #1469 | C2×C89 | semidirect |
| 189. #1302 | C2×C89 | semidirect |
| 190. C89 | #10140 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3226 | 2 |
| C89×#3213 | 2 |
| C2×#489×C89 | 2 |
| C89×#1558 | 2 |
| C89×#1530 | 2 |
| C89×#1469 | 2 |
| C89×#1302 | 2 |
| #10140 | 89 |