Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1170 conjugacy classes of subgroups; only the 390 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 390 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 | C2×C9 | C22×C42 |
| Frattini, socle | C23×C3 | C23×D3 |
| Fitting | C9×#376 | C2 |
| prime radical | C22×D36 | C22 |
| cosocle | C23×C9 | C24 |
| hypercenter | #376 | D9 |
| hypocenter | C9 | #2275 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#376 | C2 | semidirect |
| 3. C4×C4⋊Dic9 | C2 | semidirect |
| 4. #10588346 | C2 | semidirect |
| 5. D9×#95 | C2 | semidirect |
| 13. C4×D36 | C4 | semidirect |
| 29. C2×C4×D9 | C2×C4 | semidirect |
| 30. C42×C9 | C2×C4 | semidirect |
| 31. (C2×D9)⋊C4 | C2×C4 | semidirect |
| 32. C4⋊Dic9 | C2×C4 | semidirect |
| 57. D36 | C42 | semidirect |
| 62. #376 | D9 | semidirect |
| 125. C42 | C4×D9 | semidirect |
| 136. C9 | #2275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D36 | 2 |
| C9×#376 | 2 |
| C4×C4⋊Dic9 | 2 |
| #10588346 | 2 |
| D9×#95 | 2 |
| #73412 | 3 |