Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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×D233 |
| commutator, socle, cosocle | C22×C233 | C24 |
| Fitting | C4⋊Q8×C233 | C2 |
| prime radical | C2×D932 | C22 |
| hypercenter | C4⋊Q8 | D233 |
| hypocenter | C233 | #554 |
| LCS | G ▷ C22×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21418526 | C2 | semidirect |
| 2. #21418515 | C2 | semidirect |
| 3. #21418511 | C2 | semidirect |
| 4. C4×Dic466 | C2 | semidirect |
| 7. C4⋊C4×D233 | C2 | semidirect |
| 8. C4⋊Q8×C233 | C2 | semidirect |
| 27. D932 | Q8 | semidirect |
| 53. C233 | #554 | semidirect |
| 55. C4⋊Q8 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418526 | 2 |
| #21418515 | 2 |
| #21418511 | 2 |
| C4×Dic466 | 2 |
| C4×D932 | 2 |
| #21418497 | 2 |
| C4⋊C4×D233 | 2 |
| C4⋊Q8×C233 | 2 |
| #554 | 233 |