Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 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, socle, cosocle | C23×C23 | C24 |
| Fitting | C23×#395 | C2 |
| hypercenter | #395 | D23 |
| hypocenter | C23 | #2388 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#67292 | C2 | semidirect |
| 2. C2×#10625064 | C2 | semidirect |
| 3. #13092334 | C2 | semidirect |
| 4. #13092328 | C2 | semidirect |
| 5. #13092327 | C2 | semidirect |
| 6. #13092264 | C2 | semidirect |
| 7. C23×#395 | C2 | semidirect |
| 38. C2×C4×D23 | D4 | semidirect |
| 52. C22×D23 | #41 | semidirect |
| 59. C2×C4×C23 | #41 | semidirect |
| 86. #395 | D23 | semidirect |
| 110. C23 | #2388 | semidirect |
| 155. C2×C4 | #67292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67292 | 2 |
| C2×#10625064 | 2 |
| #13092334 | 2 |
| #13092328 | 2 |
| #13092327 | 2 |
| #13092264 | 2 |
| C23×#395 | 2 |
| #2388 | 23 |