Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1660 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 1063 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. #5827 | C2 | semidirect |
| 3. Dic3×#41 | C2 | semidirect |
| 4. #5798 | C2 | semidirect |
| 5. C2×D4×Dic3 | C2 | semidirect |
| 7. C3×H(5,𝔽2) | C4 | semidirect |
| 10. C23×Dic3 | C22 | semidirect |
| 11. C2×#217 | C22 | semidirect |
| 12. Q8×Dic3 | C22 | semidirect |
| 13. Q8×Dic3 | C22 | semidirect |
| 14. D4×Dic3 | C22 | semidirect |
| 15. D4×Dic3 | C22 | semidirect |
| 16. D4×Dic3 | C22 | semidirect |
| 17. #926 | C22 | semidirect |
| 18. C2×C4⋊Dic3 | C22 | semidirect |
| 19. C2×C4×Dic3 | C22 | semidirect |
| 26. C3×#41 | C2×C4 | semidirect |
| 28. C2×C3×D4 | C2×C4 | semidirect |
| 40. H(5,𝔽2) | Dic3 | direct (N × H) |
| 55. C23×C3 | C22×C4 | semidirect |
| 57. C3×Q8 | C22×C4 | semidirect |
| 58. C3×D4 | C22×C4 | semidirect |
| 59. C2×C3×C4 | C22×C4 | semidirect |
| 68. #41 | C2×Dic3 | semidirect |
| 70. C2×D4 | C2×Dic3 | semidirect |
| 90. Dic3 | H(5,𝔽2) | direct (N × H) |
| 93. C23 | C22×Dic3 | semidirect |
| 95. Q8 | C22×Dic3 | semidirect |
| 96. D4 | C22×Dic3 | semidirect |
| 103. C2×C4 | C22×Dic3 | semidirect |
| 118. C3 | C4×H(5,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×H(5,𝔽2) | 2 |
| #5827 | 2 |
| Dic3×#41 | 2 |
| #5798 | 2 |
| C2×D4×Dic3 | 2 |
| C4×H(5,𝔽2) | 3 |