Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5828 | C2 | semidirect |
| 2. C2×#950 | C2 | semidirect |
| 3. C22×ΓL(1,𝔽25) | C2 | semidirect |
| 4. #5524 | C2 | semidirect |
| 5. C3×#416 | C2 | semidirect |
| 6. #5113 | C2 | semidirect |
| 7. #4998 | C2 | semidirect |
| 8. #4816 | C2 | semidirect |
| 9. #4812 | C2 | semidirect |
| 10. #4782 | C2 | semidirect |
| 11. #4780 | C2 | semidirect |
| 20. C2×#216 | C22 | semidirect |
| 21. C2×#215 | C22 | semidirect |
| 25. C2×#214 | C22 | semidirect |
| 26. C2×#213 | C22 | semidirect |
| 38. C3×#103 | C22 | semidirect |
| 39. C3×#102 | C22 | semidirect |
| 40. #821 | C22 | semidirect |
| 41. #816 | C22 | semidirect |
| 42. #808 | C22 | semidirect |
| 43. #807 | C22 | semidirect |
| 54. #416 | D3 | semidirect |
| 94. C2×C3⋊C8 | D4 | semidirect |
| 127. #103 | C2×D3 | semidirect |
| 129. #102 | C2×D3 | semidirect |
| 290. C3 | #3054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5828 | 2 |
| C2×#950 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| #5524 | 2 |
| C3×#416 | 2 |
| #5113 | 2 |
| #4998 | 2 |
| #4816 | 2 |
| #4812 | 2 |
| #4782 | 2 |
| #4780 | 2 |
| #3054 | 3 |