Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C23×D43 |
| commutator, socle, cosocle | C22×C43 | C24 |
| Fitting | C22⋊Q8×C43 | C2 |
| hypercenter | C22⋊Q8 | D43 |
| hypocenter | C43 | #538 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13063320 | C2 | semidirect |
| 2. #13063314 | C2 | semidirect |
| 3. #13063310 | C2 | semidirect |
| 4. #13063300 | C2 | semidirect |
| 5. #13063299 | C2 | semidirect |
| 6. #13063295 | C2 | semidirect |
| 7. (C22⋊D43)⋊C4 | C2 | semidirect |
| 8. C2×(C2×D43)⋊C4 | C2 | semidirect |
| 9. C22⋊Q8×C43 | C2 | semidirect |
| 11. C2×Q8×C43 | C22 | semidirect |
| 17. C2×D172 | C22 | semidirect |
| 18. C2×C4×D43 | C22 | semidirect |
| 19. C4⋊C4×C43 | C22 | semidirect |
| 20. C4⋊C4×C43 | C22 | semidirect |
| 26. (C2×D43)⋊C4 | C22 | semidirect |
| 27. (C2×D43)⋊C4 | C22 | semidirect |
| 28. C4⋊Dic43 | C22 | semidirect |
| 29. Dic43⋊C4 | C22 | semidirect |
| 30. C4×Dic43 | C22 | semidirect |
| 75. C43 | #538 | semidirect |
| 79. C22⋊Q8 | D43 | semidirect |
| 86. C2×Q8 | C2×D43 | semidirect |
| 96. C4⋊C4 | C2×D43 | semidirect |
| 97. C4⋊C4 | C2×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063320 | 2 |
| #13063314 | 2 |
| #13063310 | 2 |
| #13063300 | 2 |
| #13063299 | 2 |
| #13063295 | 2 |
| (C22⋊D43)⋊C4 | 2 |
| C2×(C2×D43)⋊C4 | 2 |
| C22⋊Q8×C43 | 2 |
| #538 | 43 |