Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D23 |
| commutator | C22×C23 | C22×C4 |
| Fitting | C23×#95 | C2 |
| socle, cosocle | C23×C23 | C23 |
| prime radical | C23×D23 | C22 |
| hypercenter | #95 | D23 |
| hypocenter | C23 | #381 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C23×#95 | C2 | semidirect |
| 4. C23⋊#95 | C2 | semidirect |
| 5. C23⋊#95 | C2 | semidirect |
| 12. C2×C4×D23 | C4 | semidirect |
| 56. #95 | D23 | semidirect |
| 57. C23 | #381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D23 | 2 |
| C2×(C2×D23)⋊C4 | 2 |
| C23×#95 | 2 |
| C23⋊#95 | 2 |
| #381 | 23 |