Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1854 conjugacy classes of subgroups; only the 894 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 894 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C89 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C89 |
| prime radical | C25×C89 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89×#2493 | C2 | semidirect |
| 8. #401×C89 | C22 | semidirect |
| 9. #400×C89 | C22 | semidirect |
| 10. #387×C89 | C22 | semidirect |
| 13. #383×C89 | C22 | semidirect |
| 81. #35456 | C89 | direct (N × H) |
| 85. #2493 | C2×C89 | semidirect |
| 89. C89 | #35456 | direct (N × H) |
| 93. #401 | C22×C89 | semidirect |
| 94. #400 | C22×C89 | semidirect |
| 95. #387 | C22×C89 | semidirect |
| 98. #383 | C22×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2493 | 2 |
| C89×#2315 | 2 |
| C2×#381×C89 | 2 |
| C89×#2273 | 2 |
| #35456 | 89 |