Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
126 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D3 |
| commutator, socle, prime radical | C22×C3 | C22×C8 |
| Fitting | C3×C4⋊C16 | C2 |
| cosocle | C2×C3×C8 | C23 |
| hypercenter | C4⋊C16 | D3 |
| hypocenter | C3 | #2183 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C8 ◁ C4⋊C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 41. C3⋊C16 | Q8 | semidirect |
| 115. C3 | #2183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic6 | 2 |
| C3×C4⋊C16 | 2 |
| #4502 | 2 |
| Dic3⋊C16 | 2 |
| Dic3×C16 | 2 |
| #4461 | 2 |
| #2183 | 3 |