Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
435 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 435 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D9 |
| commutator, cosocle | C22×C9 | C24 |
| Frattini, socle | C22×C3 | C23×D3 |
| Fitting | C2×C9×#41 | C2 |
| hypercenter | C2×#41 | D9 |
| hypocenter | C9 | #548 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9×#41 | C2 | semidirect |
| 2. C2×Q8×D9 | C2 | semidirect |
| 3. Q8×Dic9 | C2 | semidirect |
| 4. #63500 | C2 | semidirect |
| 5. #63498 | C2 | semidirect |
| 6. C4×#611 | C2 | semidirect |
| 7. #63486 | C2 | semidirect |
| 32. Q8×C9 | D4 | semidirect |
| 64. C2×D9 | #41 | semidirect |
| 70. C2×#41 | D9 | semidirect |
| 121. C9 | #548 | semidirect |
| 125. Q8 | #611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#41 | 2 |
| C2×Q8×D9 | 2 |
| Q8×Dic9 | 2 |
| #63500 | 2 |
| #63498 | 2 |
| C4×#611 | 2 |
| #63486 | 2 |
| #5831 | 3 |