Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Fitting | C23×C22⋊Q8 | C2 |
| prime radical | #10625055 | C2 |
| hypercenter | C22⋊Q8 | D23 |
| hypocenter | C23 | #542 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊Q8 | C2 | semidirect |
| 2. #10625118 | C2 | semidirect |
| 3. #10625115 | C2 | semidirect |
| 4. #10625100 | C2 | semidirect |
| 5. C4×C22⋊D23 | C2 | semidirect |
| 6. #10625069 | C2 | semidirect |
| 7. #10625067 | C2 | semidirect |
| 8. #10625067 | C2 | semidirect |
| 9. #10625065 | C2 | semidirect |
| 10. #10625063 | C2 | semidirect |
| 11. #10625058 | C2 | semidirect |
| 12. #10625056 | C2 | semidirect |
| 13. #10625056 | C2 | semidirect |
| 15. #10625050 | C2 | semidirect |
| 114. C22⋊Q8 | D23 | semidirect |
| 119. C23 | #542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊Q8 | 2 |
| #10625118 | 2 |
| #10625115 | 2 |
| #10625100 | 2 |
| C4×C22⋊D23 | 2 |
| #10625069 | 2 |
| #10625067 | 2 |
| #10625065 | 2 |
| #10625063 | 2 |
| #10625058 | 2 |
| #10625056 | 2 |
| #10625055 | 2 |
| #10625050 | 2 |
| #542 | 23 |