Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
141 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 42 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×D9 |
| commutator, cosocle | C22×C9 | C23 |
| Frattini, socle | C22×C3 | C22×D3 |
| Fitting | C9×C22⋊C4 | C2 |
| hypercenter | C22⋊C4 | D9 |
| hypocenter | C9 | #121 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#611 | C2 | semidirect |
| 2. C2×#611 | C2 | semidirect |
| 3. C2×D36 | C2 | semidirect |
| 4. C2×C4×D9 | C2 | semidirect |
| 5. C9×C22⋊C4 | C2 | semidirect |
| 6. (C2×D9)⋊C4 | C2 | semidirect |
| 7. Dic9⋊C4 | C2 | semidirect |
| 36. C2×D9 | D4 | semidirect |
| 40. Dic9 | D4 | semidirect |
| 65. C22⋊C4 | D9 | semidirect |
| 80. C9 | #121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#611 | 2 |
| C2×D36 | 2 |
| C2×C4×D9 | 2 |
| C9×C22⋊C4 | 2 |
| (C2×D9)⋊C4 | 2 |
| Dic9⋊C4 | 2 |
| #884 | 3 |