Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1564 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1564 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, socle, cosocle | C23×C23 | C24 |
| Fitting | C23×#379 | C2 |
| hypercenter | #379 | D23 |
| hypocenter | C23 | #2403 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D23 | C2 | semidirect |
| 2. C2×#10625053 | C2 | semidirect |
| 3. #13092326 | C2 | semidirect |
| 4. #13092294 | C2 | semidirect |
| 5. C23×#379 | C2 | semidirect |
| 7. C24×D23 | C22 | semidirect |
| 11. C22×C22⋊D23 | C22 | semidirect |
| 12. C23×Dic23 | C22 | semidirect |
| 13. C22×D92 | C22 | semidirect |
| 14. C2×C22⋊C4×C23 | C22 | semidirect |
| 15. C2×C22⋊C4×C23 | C22 | semidirect |
| 16. C2×(C2×D23)⋊C4 | C22 | semidirect |
| 18. C23⋊#95 | C22 | semidirect |
| 21. C24×C23 | D4 | semidirect |
| 36. C2×C22⋊D23 | D4 | semidirect |
| 64. C22×D23 | C2×D4 | semidirect |
| 72. C2×Dic23 | C2×D4 | semidirect |
| 82. C22×C23 | #120 | semidirect |
| 98. #379 | D23 | semidirect |
| 115. C2×C22⋊C4 | C2×D23 | semidirect |
| 116. C2×C22⋊C4 | C2×D23 | semidirect |
| 118. C23 | #2403 | semidirect |
| 126. C24 | D92 | semidirect |
| 187. C22 | #10625053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D23 | 2 |
| C2×#10625053 | 2 |
| #13092326 | 2 |
| #13092294 | 2 |
| C23×#379 | 2 |
| #2403 | 23 |