Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1637 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 1637 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×(C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C9 | C24 |
| Frattini | C2×C3 | C23×S4 |
| Fitting | C22×C3×#41 | D3 |
| socle | C23×C3 | C2×S4 |
| hypercenter | C22×C4 | (C22⋊C9)⋊C2 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#41⋊C9 | C2 | semidirect |
| 2. C2×#63692 | C2 | direct (N × H) |
| 3. C22×#3689 | C2 | semidirect |
| 6. C2×#41⋊C9 | C22 | semidirect |
| 7. C22×Q8⋊C9 | C22 | semidirect |
| 8. #63692 | C22 | direct (N × H) |
| 9. C2×#3689 | C22 | semidirect |
| 20. #41⋊C9 | C23 | semidirect |
| 21. C2×Q8⋊C9 | C23 | semidirect |
| 22. #3689 | C23 | semidirect |
| 46. Q8⋊C9 | C24 | semidirect |
| 47. C22×#41 | D9 | semidirect |
| 86. C2×#41 | C2×D9 | semidirect |
| 131. #41 | C22×D9 | semidirect |
| 191. C22 | #63692 | direct (N × H) |
| 199. C2 | C2×#63692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41⋊C9 | 2 |
| C2×#63692 | 2 |
| C22×#3689 | 2 |
| C22×#949 | 3 |
| C22×D36 | 4 |