Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
4086 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 4086 conjugacy classes of subgroups — too many to draw. Only its 811 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D89 |
| commutator, socle, cosocle | C23×C89 | C25 |
| Fitting | C89×#2868 | C2 |
| hypercenter | #2868 | D89 |
| hypocenter | C89 | #36644 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #2868 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19152149 | C2 | semidirect |
| 2. #26028647 | C2 | semidirect |
| 3. #26028610 | C2 | semidirect |
| 4. #26028598 | C2 | semidirect |
| 5. #26022814 | C2 | semidirect |
| 6. C43×D89 | C2 | semidirect |
| 7. C89×#2868 | C2 | semidirect |
| 40. C42×D89 | D4 | semidirect |
| 69. C42×C89 | #41 | semidirect |
| 88. C4×D89 | #127 | semidirect |
| 97. C4×C89 | #532 | semidirect |
| 106. #2868 | D89 | semidirect |
| 112. C89 | #36644 | semidirect |
| 174. C42 | #13083575 | semidirect |
| 204. C4 | #19152149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152149 | 2 |
| #26028647 | 2 |
| #26028610 | 2 |
| #26028598 | 2 |
| #26022814 | 2 |
| C43×D89 | 2 |
| C89×#2868 | 2 |
| #36644 | 89 |