Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D9 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini, socle | C23×C3 | C23×D3 |
| Fitting | C9×#396 | C2 |
| prime radical | C24×C3 | C22×D3 |
| hypercenter | #396 | D9 |
| hypocenter | C9 | #2401 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ #396 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10588666 | C2 | semidirect |
| 3. C4⋊C4×Dic9 | C2 | semidirect |
| 6. C9⋊#401 | C2 | semidirect |
| 7. #10588328 | C2 | semidirect |
| 171. C9 | #2401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#396 | 2 |
| #10588666 | 2 |
| C4⋊C4×Dic9 | 2 |
| #10588633 | 2 |
| C22⋊C4×Dic9 | 2 |
| C9⋊#401 | 2 |
| #10588328 | 2 |
| #77283 | 3 |