Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D23 |
| commutator, socle, prime radical | C23×C23 | C22×C4 |
| Fitting | C23×#336 | C2 |
| cosocle | C22×C4×C23 | C23 |
| hypercenter | #336 | D23 |
| hypocenter | C23 | #1917 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 122. C23 | #1917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic23⋊C8 | 2 |
| C2×#10624997 | 2 |
| C4×C4⋊Dic23 | 2 |
| #13092172 | 2 |
| #13092171 | 2 |
| C23×#336 | 2 |
| #1917 | 23 |