Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×#384 | C2 |
| socle, cosocle | C23×C23 | C24 |
| prime radical | C22×D92 | C22 |
| hypercenter | #384 | D23 |
| hypocenter | C23 | #2326 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#10625058 | C2 | semidirect |
| 4. #13092322 | C2 | semidirect |
| 6. #13092307 | C2 | semidirect |
| 7. #13092288 | C2 | semidirect |
| 8. #13092263 | C2 | semidirect |
| 9. C23×#384 | C2 | semidirect |
| 26. #10625046 | C4 | semidirect |
| 46. C2×Dic46 | C2×C4 | semidirect |
| 50. C42×C23 | C2×C4 | semidirect |
| 53. (C2×D23)⋊C4 | C2×C4 | semidirect |
| 113. #384 | D23 | semidirect |
| 141. C23 | #2326 | semidirect |
| 169. C42 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625046 | 2 |
| C2×#10625058 | 2 |
| C2×#10625064 | 2 |
| #13092322 | 2 |
| #13092318 | 2 |
| #13092307 | 2 |
| #13092288 | 2 |
| #13092263 | 2 |
| C23×#384 | 2 |
| #2326 | 23 |