Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
265 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#859 | C2 | semidirect |
| 5. C22×SL(2,𝔽3) | C4 | semidirect |
| 24. C22×Q8 | Dic3 | semidirect |
| 44. SL(2,𝔽3) | C22⋊C4 | semidirect |
| 94. Q8 | #217 | semidirect |
| 118. C22 | #859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×SL(2,𝔽3) | 2 |
| C2×#859 | 2 |
| #1787 | 3 |
| C2×#217 | 4 |