Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C3×SD16 | C2 | semidirect |
| 2. #5812 | C2 | semidirect |
| 3. C2×#942 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. #5166 | C2 | semidirect |
| 7. #5163 | C2 | semidirect |
| 8. #5113 | C2 | semidirect |
| 9. #5102 | C2 | semidirect |
| 19. Q8×Dic3 | C22 | semidirect |
| 20. C2×#216 | C22 | semidirect |
| 22. C2×#215 | C22 | semidirect |
| 31. #821 | C22 | semidirect |
| 32. #816 | C22 | semidirect |
| 33. Dic3⋊C8 | C22 | semidirect |
| 35. C22×SD16 | D3 | semidirect |
| 46. C2×C3×Q8 | D4 | semidirect |
| 135. C2×Q8 | #67 | semidirect |
| 227. C3 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×SD16 | 2 |
| #5812 | 2 |
| C2×#942 | 2 |
| #5805 | 2 |
| #5215 | 2 |
| #5166 | 2 |
| #5163 | 2 |
| #5113 | 2 |
| #5102 | 2 |
| #3043 | 3 |