Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. C3×#424 | C2 | semidirect |
| 3. #5124 | C2 | semidirect |
| 5. #5102 | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 24. #424 | D3 | semidirect |
| 173. C3 | #2098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#424 | 2 |
| #5139 | 2 |
| #5124 | 2 |
| #5110 | 2 |
| #5102 | 2 |
| #5005 | 2 |
| #4531 | 2 |
| #2098 | 3 |