Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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, prime radical, cosocle | C23×C3 | C24 |
| Fitting | C3×#389 | C2 |
| hypercenter | #389 | D3 |
| hypocenter | C3 | #2734 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 59. C3×C4⋊C4 | Q8 | semidirect |
| 64. C4⋊Dic3 | Q8 | semidirect |
| 145. C4⋊C4 | Dic6 | semidirect |
| 217. C3 | #2734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#888 | 2 |
| C3×#389 | 2 |
| #4982 | 2 |
| #4980 | 2 |
| #4979 | 2 |
| #4929 | 2 |
| #4928 | 2 |
| #4656 | 2 |
| #4654 | 2 |
| #2734 | 3 |