Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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×H(5,𝔽2) | C2 | semidirect |
| 2. #5964 | C2 | semidirect |
| 3. #5836 | C2 | semidirect |
| 4. #5835 | C2 | semidirect |
| 5. #5822 | C2 | semidirect |
| 6. #5819 | C2 | semidirect |
| 7. C2×#932 | C2 | semidirect |
| 10. C3×H(5,𝔽2) | C22 | semidirect |
| 13. C2×C3×#41 | C22 | semidirect |
| 15. C22×C3×D4 | C22 | semidirect |
| 16. #1010 | C22 | semidirect |
| 17. #1009 | C22 | semidirect |
| 21. C2×#235 | C22 | semidirect |
| 22. #951 | C22 | semidirect |
| 23. #950 | C22 | semidirect |
| 24. #949 | C22 | semidirect |
| 25. #948 | C22 | semidirect |
| 26. #942 | C22 | semidirect |
| 27. C2×#214 | C22 | semidirect |
| 28. #932 | C22 | semidirect |
| 29. #932 | C22 | semidirect |
| 30. C2×#213 | C22 | semidirect |
| 31. C2×#208 | C22 | semidirect |
| 33. C2×H(5,𝔽2) | D3 | semidirect |
| 64. #235 | C23 | semidirect |
| 65. C2×D12 | C23 | semidirect |
| 67. C2×Dic6 | C23 | semidirect |
| 68. #216 | C23 | semidirect |
| 69. #215 | C23 | semidirect |
| 70. #214 | C23 | semidirect |
| 71. #213 | C23 | semidirect |
| 73. #208 | C23 | semidirect |
| 74. C2×C3⋊C8 | C23 | semidirect |
| 80. H(5,𝔽2) | C2×D3 | semidirect |
| 85. C2×#41 | C2×D3 | semidirect |
| 87. C22×D4 | C2×D3 | semidirect |
| 223. C3 | #3585 | 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 |
| #5964 | 2 |
| #5836 | 2 |
| #5835 | 2 |
| #5822 | 2 |
| #5819 | 2 |
| C2×#932 | 2 |
| #3585 | 3 |