Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
512 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 189 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×D23 |
| commutator | C22×C23 | C23×C4 |
| Fitting | C23×#381 | C2 |
| socle, cosocle | C23×C23 | C24 |
| prime radical | C24×C23 | C23 |
| hypercenter | #381 | D23 |
| hypocenter | C23 | #2313 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13092302 | C2 | semidirect |
| 3. #13092300 | C2 | semidirect |
| 13. C2×C4⋊Dic23 | C4 | semidirect |
| 108. C23 | #2313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic23 | 2 |
| #13092302 | 2 |
| #13092300 | 2 |
| #13092280 | 2 |
| #13092275 | 2 |
| C22⋊C4×Dic23 | 2 |
| C23×#381 | 2 |
| #2313 | 23 |