Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
908 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
| prime radical | C24×D23 | C22 |
| hypercenter | #399 | D23 |
| hypocenter | C23 | C2×#399 |
| 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×C4⋊C4×D23 | C2 | semidirect |
| 3. #13092354 | C2 | semidirect |
| 4. #13092353 | C2 | semidirect |
| 5. #13092352 | C2 | semidirect |
| 6. #95×D23 | C2 | semidirect |
| 7. C23×#399 | C2 | semidirect |
| 11. C2×C4⋊C4×C23 | C22 | semidirect |
| 16. C2×C4⋊Dic23 | C22 | semidirect |
| 17. C2×Dic23⋊C4 | C22 | semidirect |
| 20. C23×#95 | C22 | semidirect |
| 21. C23⋊#95 | C22 | semidirect |
| 89. #399 | D23 | direct (N × H) |
| 96. D23 | #399 | direct (N × H) |
| 103. C2×C4⋊C4 | C2×D23 | semidirect |
| 110. #95 | C2×D23 | semidirect |
| 111. C23 | C2×#399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D23 | 2 |
| C2×C22⋊C4×D23 | 2 |
| #13092354 | 2 |
| #13092353 | 2 |
| #13092352 | 2 |
| #95×D23 | 2 |
| C23×#399 | 2 |
| C2×#399 | 23 |