Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 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×D233 |
| commutator, socle, cosocle | C22×C233 | C24 |
| Fitting | C4⋊Q8×C233 | C2 |
| prime radical | #21418510 | C2 |
| hypercenter | C4⋊Q8 | D233 |
| hypocenter | C233 | #542 |
| 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. #21418530 | C2 | semidirect |
| 2. #21418524 | C2 | semidirect |
| 3. #21418523 | C2 | semidirect |
| 4. #21418520 | C2 | semidirect |
| 5. #21418515 | C2 | semidirect |
| 6. #21418511 | C2 | semidirect |
| 8. #21418500 | C2 | semidirect |
| 9. #21418497 | C2 | semidirect |
| 10. #21418492 | C2 | semidirect |
| 11. C4⋊Q8×C233 | C2 | semidirect |
| 73. C233 | #542 | semidirect |
| 75. C4⋊Q8 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418530 | 2 |
| #21418524 | 2 |
| #21418523 | 2 |
| #21418520 | 2 |
| #21418515 | 2 |
| #21418511 | 2 |
| #21418510 | 2 |
| #21418500 | 2 |
| #21418497 | 2 |
| #21418492 | 2 |
| C4⋊Q8×C233 | 2 |
| #542 | 233 |