Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1634 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1634 conjugacy classes of subgroups — too many to draw. Only its 272 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 | C23×#64408 |
| commutator, socle | C23×C73 | C23×C4 |
| Fitting | #395×C73 | C4 |
| prime radical, cosocle | C23×D73 | C24 |
| hypercenter | #395 | #64408 |
| hypocenter | C73 | #14302 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. #17988508 | C4 | semidirect |
| 22. #17988507 | C4 | semidirect |
| 23. #17988506 | C4 | semidirect |
| 25. #395×C73 | C4 | semidirect |
| 188. C73 | #14302 | semidirect |
| 198. #395 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×#64408 | 2 |
| C2×#17989536 | 2 |
| #22625121 | 2 |
| #22625117 | 2 |
| #22625116 | 2 |
| #22625106 | 2 |
| #395×D73 | 2 |
| #14302 | 73 |