Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1252 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 269 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, cosocle | C23×C3 | C24 |
| Frattini | C23 | C23×D3 |
| Fitting, prime radical | C23×C3×D4 | C2 |
| socle | C24×C3 | C23 |
| hypercenter | C23×D4 | D3 |
| hypocenter | C3 | C2×#394 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#217 | C2 | semidirect |
| 3. C22×#217 | C2 | semidirect |
| 4. C22×Dic3⋊C4 | C2 | semidirect |
| 5. #5222 | C2 | direct (N × H) |
| 6. C2×C3⋊#95 | C2 | semidirect |
| 18. C2×#217 | C22 | semidirect |
| 19. C2×#217 | C22 | semidirect |
| 21. C2×Dic3⋊C4 | C22 | semidirect |
| 22. C3⋊#95 | C22 | semidirect |
| 51. C22×Dic3 | D4 | semidirect |
| 107. C2×Dic3 | C2×D4 | semidirect |
| 195. C2×C3 | #394 | semidirect |
| 223. C3 | C2×#394 | semidirect |
| 225. C2 | #5222 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D4 | 2 |
| C22×#217 | 2 |
| C22×Dic3⋊C4 | 2 |
| #5222 | 2 |
| C2×C3⋊#95 | 2 |
| C2×#394 | 3 |