Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1803 conjugacy classes of subgroups; only the 582 normal subgroups are shown.
This group has 1803 conjugacy classes of subgroups — too many to draw. Only its 582 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | Q82×C9 | C2 |
| hypercenter | Q82 | D9 |
| hypocenter | C9 | #3483 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q82×C9 | C2 | semidirect |
| 2. #10589836 | C2 | semidirect |
| 3. #10589827 | C2 | semidirect |
| 4. #10589679 | C2 | semidirect |
| 5. C4×#3701 | C2 | semidirect |
| 53. Q8×C9 | #41 | semidirect |
| 62. Q82 | D9 | semidirect |
| 135. C9 | #3483 | semidirect |
| 138. Q8 | #3701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q82×C9 | 2 |
| #10589836 | 2 |
| #10589827 | 2 |
| #10589679 | 2 |
| C4×#3701 | 2 |
| #87040 | 3 |