Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
1495 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1495 conjugacy classes of subgroups — too many to draw. Only its 268 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C9⋊D9 |
| commutator, cosocle | C22×C92 | C23 |
| Frattini, socle | C22×C32 | C22×C3⋊D3 |
| Fitting | C92×C22⋊C4 | C2 |
| hypercenter | C22⋊C4 | C9⋊D9 |
| hypocenter | C92 | #120 |
| LCS | G ▷ C22×C92 ▷ C92 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C9⋊D9 | C2 | semidirect |
| 2. C2×#10619673 | C2 | semidirect |
| 3. C2×C4⋊(C9⋊D9) | C2 | semidirect |
| 4. C92×C22⋊C4 | C2 | semidirect |
| 5. #13046768 | C2 | semidirect |
| 11. C22×C9⋊D9 | C22 | semidirect |
| 12. C2×C4×C92 | C22 | semidirect |
| 14. C2×C9⋊Dic9 | C22 | semidirect |
| 22. C22×C92 | D4 | semidirect |
| 29. C2×C9⋊D9 | D4 | semidirect |
| 56. C9×C22⋊C4 | D9 | semidirect |
| 70. C92 | #120 | semidirect |
| 85. C2×C4×C9 | C2×D9 | semidirect |
| 111. C22×C9 | D36 | semidirect |
| 146. C22⋊C4 | C9⋊D9 | semidirect |
| 159. C9 | #63444 | semidirect |
| 168. C2×C4 | C2×C9⋊D9 | semidirect |
| 181. C22 | C4⋊(C9⋊D9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C9⋊D9 | 2 |
| C2×#10619673 | 2 |
| C2×C4⋊(C9⋊D9) | 2 |
| C92×C22⋊C4 | 2 |
| #13046768 | 2 |
| #11721728 | 3 |