Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D23 |
| commutator, socle, cosocle | C22×C23 | C25 |
| Fitting | C23×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D23 |
| hypocenter | C23 | #3529 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13093167 | C2 | semidirect |
| 2. #13093161 | C2 | semidirect |
| 3. #13093156 | C2 | semidirect |
| 4. #13092966 | C2 | semidirect |
| 5. #13092946 | C2 | semidirect |
| 6. #13092923 | C2 | semidirect |
| 7. C23×H(3,𝔽4) | C2 | semidirect |
| 8. C23×Dic23 | C22 | semidirect |
| 9. C2×#67292 | C22 | semidirect |
| 14. #10625124 | C22 | semidirect |
| 15. #10625117 | C22 | semidirect |
| 16. Q8×Dic23 | C22 | semidirect |
| 17. #10625115 | C22 | semidirect |
| 23. #10625057 | C22 | semidirect |
| 24. #10625055 | C22 | semidirect |
| 25. #10625054 | C22 | semidirect |
| 26. (C22⋊D23)⋊C4 | C22 | semidirect |
| 27. #10625050 | C22 | semidirect |
| 28. #10625049 | C22 | semidirect |
| 29. #10625048 | C22 | semidirect |
| 30. #10625046 | C22 | semidirect |
| 31. C42×D23 | C22 | semidirect |
| 32. #10625041 | C22 | semidirect |
| 96. H(3,𝔽4) | D23 | semidirect |
| 130. C23 | #3529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13093167 | 2 |
| #13093161 | 2 |
| #13093156 | 2 |
| #13092966 | 2 |
| #13092946 | 2 |
| #13092923 | 2 |
| C23×H(3,𝔽4) | 2 |
| #3529 | 23 |