Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
3464 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D3 |
| commutator | C22×C3 | C23×C4 |
| Frattini | C23 | C23×D3 |
| Fitting, prime radical | C26×C3 | C2 |
| socle | C24×C3 | C23 |
| cosocle | C23×C3 | C24 |
| hypercenter | C26 | D3 |
| hypocenter | C3 | C2×#379 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C26 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#217 | C2 | semidirect |
| 3. #5247 | C2 | direct (N × H) |
| 6. C25×C3 | C4 | semidirect |
| 9. C23×Dic3 | C22 | semidirect |
| 11. C2×#217 | C22 | semidirect |
| 20. C24×C3 | C2×C4 | semidirect |
| 25. C22×Dic3 | C23 | semidirect |
| 28. C25 | Dic3 | semidirect |
| 40. C23×C3 | C22⋊C4 | semidirect |
| 53. C24 | C2×Dic3 | semidirect |
| 65. C22×C3 | C2×C22⋊C4 | semidirect |
| 76. C23 | #217 | semidirect |
| 85. C2×C3 | #379 | semidirect |
| 93. C22 | C2×#217 | semidirect |
| 98. C3 | C2×#379 | semidirect |
| 100. C2 | #5247 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C26×C3 | 2 |
| C22×#217 | 2 |
| #5247 | 2 |
| C2×#379 | 3 |