Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
924 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 189 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, socle, cosocle | C23×C3 | C24 |
| Fitting | C3×#390 | C2 |
| hypercenter | #390 | D3 |
| hypocenter | C3 | #2856 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#940 | C2 | semidirect |
| 2. C2×#938 | C2 | semidirect |
| 3. C2×#895 | C2 | semidirect |
| 4. C2×#884 | C2 | semidirect |
| 5. C2×C42×D3 | C2 | semidirect |
| 6. C3×#390 | C2 | semidirect |
| 7. #4975 | C2 | semidirect |
| 8. #4957 | C2 | semidirect |
| 9. #4939 | C2 | semidirect |
| 40. #390 | D3 | semidirect |
| 68. C2×C4×D3 | D4 | semidirect |
| 69. C2×C4×D3 | D4 | semidirect |
| 79. C4×Dic3 | D4 | semidirect |
| 198. C2×D3 | #127 | semidirect |
| 201. C3×C4 | #121 | semidirect |
| 204. Dic3 | #121 | semidirect |
| 277. C4 | #884 | semidirect |
| 278. C3 | #2856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#940 | 2 |
| C2×#938 | 2 |
| C2×#895 | 2 |
| C2×#884 | 2 |
| C2×C42×D3 | 2 |
| C3×#390 | 2 |
| #4975 | 2 |
| #4957 | 2 |
| #4939 | 2 |
| #2856 | 3 |