Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
116 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #99 |
| commutator | C22×C4 | C2×C3×C4 |
| Frattini, cosocle | C2×C4⋊C4 | C22×C3 |
| prime radical | C23×C3 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1353 | C3 | direct (N × H) |
| 103. C3 | #1353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#400 | 2 |
| C3×#343 | 2 |
| C3×#324 | 2 |
| #1353 | 3 |