Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1416 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 210 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×#395 | C2 |
| hypercenter | #395 | D9 |
| hypocenter | C9 | #2388 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#3701 | C2 | semidirect |
| 2. C2×#63455 | C2 | semidirect |
| 3. C9×#395 | C2 | semidirect |
| 4. #10588911 | C2 | semidirect |
| 5. #10588671 | C2 | semidirect |
| 6. #10588351 | C2 | semidirect |
| 7. #10588346 | C2 | semidirect |
| 46. C2×C4×D9 | D4 | semidirect |
| 75. C22×D9 | #41 | semidirect |
| 82. C2×C4×C9 | #41 | semidirect |
| 92. #395 | D9 | semidirect |
| 215. C9 | #2388 | semidirect |
| 238. C2×C4 | #3701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3701 | 2 |
| C2×#63455 | 2 |
| C9×#395 | 2 |
| #10588911 | 2 |
| #10588671 | 2 |
| #10588351 | 2 |
| #10588346 | 2 |
| #77169 | 3 |