Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
840 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 163 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×#399 | C2 |
| hypercenter | #399 | D23 |
| hypocenter | C23 | #2397 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625064 | C2 | semidirect |
| 2. C2×(C22⋊D23)⋊C4 | C2 | semidirect |
| 3. #13092352 | C2 | semidirect |
| 4. #13092327 | C2 | semidirect |
| 5. #13092326 | C2 | semidirect |
| 6. #13092262 | C2 | semidirect |
| 7. C23×#399 | C2 | semidirect |
| 42. C4×Dic23 | D4 | semidirect |
| 85. #399 | D23 | semidirect |
| 108. C23 | #2397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625064 | 2 |
| C2×(C22⋊D23)⋊C4 | 2 |
| #13092352 | 2 |
| #13092327 | 2 |
| #13092326 | 2 |
| #13092262 | 2 |
| C23×#399 | 2 |
| #2397 | 23 |