Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5570 | C2 | semidirect |
| 3. #5093 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 5. #5069 | C2 | semidirect |
| 6. #5063 | C2 | semidirect |
| 7. #5024 | C2 | semidirect |
| 228. C3 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#554 | 2 |
| #5570 | 2 |
| #5093 | 2 |
| #5091 | 2 |
| #5069 | 2 |
| #5063 | 2 |
| #5024 | 2 |
| #5019 | 2 |
| #5018 | 2 |
| C4×#214 | 2 |
| #3372 | 3 |