Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
164 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C8 | D4 |
| commutator | C4 | C22×C3×C8 |
| Frattini, cosocle | C42 | C23×C3 |
| socle, prime radical | C22×C3 | C4×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C8 ◁ C3×C4×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C8×Q16 | C3 | direct (N × H) |
| 23. C3×Q16 | C8 | direct (N × H) |
| 56. C3×C8 | Q16 | direct (N × H) |
| 58. Q16 | C3×C8 | direct (N × H) |
| 89. C8 | C3×Q16 | direct (N × H) |
| 101. C3 | C8×Q16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×Q8 | 2 |
| C3×C4×Q16 | 2 |
| C3×#335 | 2 |
| C3×Q8⋊C8 | 2 |
| C3×C82 | 2 |
| C8×Q16 | 3 |