Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C3×#137 | C2 | semidirect |
| 2. #5832 | C2 | semidirect |
| 3. C2×#949 | C2 | semidirect |
| 4. C2×#947 | C2 | semidirect |
| 5. C2×#942 | C2 | semidirect |
| 6. C2×#908 | C2 | semidirect |
| 7. #5191 | C2 | semidirect |
| 8. #5190 | C2 | semidirect |
| 9. #5176 | C2 | semidirect |
| 10. #5168 | C2 | semidirect |
| 11. Dic3×M16 | C2 | semidirect |
| 18. C2×C3×Q16 | C22 | semidirect |
| 19. C2×C3×SD16 | C22 | semidirect |
| 25. #947 | C22 | semidirect |
| 26. #944 | C22 | semidirect |
| 27. C2×#216 | C22 | semidirect |
| 30. C2×#215 | C22 | semidirect |
| 31. #940 | C22 | semidirect |
| 33. #936 | C22 | semidirect |
| 42. #815 | C22 | semidirect |
| 43. C8×Dic3 | C22 | semidirect |
| 45. C2×#137 | D3 | semidirect |
| 82. C3×M16 | D4 | semidirect |
| 96. #208 | D4 | semidirect |
| 109. C2×Q16 | C2×D3 | semidirect |
| 113. C2×SD16 | C2×D3 | semidirect |
| 203. M16 | #67 | semidirect |
| 294. C3 | #3153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#137 | 2 |
| #5832 | 2 |
| C2×#949 | 2 |
| C2×#947 | 2 |
| C2×#942 | 2 |
| C2×#908 | 2 |
| #5191 | 2 |
| #5190 | 2 |
| #5176 | 2 |
| #5168 | 2 |
| Dic3×M16 | 2 |
| #3153 | 3 |