Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1653 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 1653 conjugacy classes of subgroups — too many to draw. Only its 294 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 | C24×C4×C9 | C2 |
| prime radical | C2×#63515 | C2 |
| hypercenter | C24×C4 | D9 |
| hypocenter | C9 | #2849 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C4×C9 | C2 | semidirect |
| 3. C2×#63491 | C2 | semidirect |
| 4. #10588927 | C2 | semidirect |
| 5. #10588893 | C2 | semidirect |
| 6. #10588891 | C2 | semidirect |
| 7. #10588890 | C2 | semidirect |
| 22. C2×(C2×D9)⋊C4 | C22 | semidirect |
| 23. C2×Dic9⋊C4 | C22 | semidirect |
| 24. C9⋊#95 | C22 | semidirect |
| 43. C22×C4×C9 | D4 | semidirect |
| 102. C24×C4 | D9 | semidirect |
| 142. C22×C9 | #123 | semidirect |
| 220. C22×C4 | #611 | semidirect |
| 246. C9 | #2849 | semidirect |
| 289. C22 | #63491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C9 | 2 |
| C2×#63515 | 2 |
| C2×#63491 | 2 |
| #10588927 | 2 |
| #10588893 | 2 |
| #10588891 | 2 |
| #10588890 | 2 |
| #84033 | 3 |