Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
| prime radical | C2×C22⋊D43 | C22 |
| hypercenter | C22⋊Q8 | D43 |
| hypocenter | C43 | D4×Q8 |
| 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. C22×Dic86 | C2 | semidirect |
| 2. C2×Q8×D43 | C2 | semidirect |
| 3. #13063324 | C2 | semidirect |
| 4. #13063323 | C2 | semidirect |
| 5. #13063305 | C2 | semidirect |
| 6. #13063303 | C2 | semidirect |
| 7. #13063302 | C2 | semidirect |
| 8. #13063290 | C2 | semidirect |
| 11. C22⋊Q8×C43 | C2 | semidirect |
| 45. C22⋊D43 | Q8 | semidirect |
| 57. Dic86 | D4 | semidirect |
| 60. C22×C43 | C2×Q8 | semidirect |
| 64. C2×D43 | C2×Q8 | semidirect |
| 73. Dic43 | C2×Q8 | semidirect |
| 80. C43 | D4×Q8 | semidirect |
| 88. C22⋊Q8 | D43 | semidirect |
| 143. C22 | Q8×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic86 | 2 |
| C2×Q8×D43 | 2 |
| #13063324 | 2 |
| #13063323 | 2 |
| #13063305 | 2 |
| #13063303 | 2 |
| #13063302 | 2 |
| #13063290 | 2 |
| C4×C22⋊D43 | 2 |
| (C22⋊D43)⋊C4 | 2 |
| C22⋊Q8×C43 | 2 |
| D4×Q8 | 43 |