Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D3 |
| commutator | C22×C3 | C23×C4 |
| Fitting | C3×#386 | C2 |
| socle, cosocle | C23×C3 | C24 |
| prime radical | C22×C3×D4 | C22 |
| hypercenter | #386 | D3 |
| hypocenter | C3 | #2372 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C4×#217 | C2 | semidirect |
| 5. #4945 | C2 | semidirect |
| 6. #4944 | C2 | semidirect |
| 7. Dic3×C22⋊C4 | C2 | semidirect |
| 8. #4648 | C2 | semidirect |
| 9. #4646 | C2 | semidirect |
| 21. #936 | C4 | semidirect |
| 60. C2×Dic6 | C2×C4 | semidirect |
| 65. #217 | C2×C4 | semidirect |
| 66. #217 | C2×C4 | semidirect |
| 71. C4×Dic3 | C2×C4 | semidirect |
| 247. C3 | #2372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#936 | 2 |
| C3×#386 | 2 |
| #5220 | 2 |
| C4×#217 | 2 |
| #4945 | 2 |
| #4944 | 2 |
| Dic3×C22⋊C4 | 2 |
| #4648 | 2 |
| #4646 | 2 |
| #2372 | 3 |