Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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×#123 | C2 |
| prime radical | C2×D4×C23 | C22 |
| hypercenter | #123 | D23 |
| hypocenter | C23 | #563 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10625095 | C2 | semidirect |
| 5. #10625060 | C2 | semidirect |
| 6. #10625059 | C2 | semidirect |
| 7. #10625050 | C2 | semidirect |
| 8. #10625050 | C2 | semidirect |
| 9. #10625049 | C2 | semidirect |
| 71. C23 | #563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#123 | 2 |
| #10625107 | 2 |
| #10625106 | 2 |
| #10625095 | 2 |
| #10625060 | 2 |
| #10625059 | 2 |
| #10625050 | 2 |
| #10625049 | 2 |
| #563 | 23 |