Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. C3×#427 | C2 | semidirect |
| 4. #5106 | C2 | semidirect |
| 5. #4998 | C2 | semidirect |
| 6. #4881 | C2 | semidirect |
| 7. #4861 | C2 | semidirect |
| 14. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 23. C3×#107 | C22 | semidirect |
| 24. C3×#106 | C22 | semidirect |
| 25. #818 | C22 | semidirect |
| 26. #817 | C22 | semidirect |
| 27. #808 | C22 | semidirect |
| 28. #807 | C22 | semidirect |
| 35. #427 | D3 | semidirect |
| 44. C2×C3×C8 | C2×C4 | semidirect |
| 56. C2×C3⋊C8 | C2×C4 | semidirect |
| 58. ΓL(1,𝔽25) | C2×C4 | semidirect |
| 59. ΓL(1,𝔽25) | C2×C4 | semidirect |
| 76. #107 | C2×D3 | semidirect |
| 79. #106 | C2×D3 | semidirect |
| 111. C2×C8 | C4×D3 | semidirect |
| 170. C3 | #2911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽25) | 2 |
| D3×#117 | 2 |
| C3×#427 | 2 |
| #5106 | 2 |
| #4998 | 2 |
| #4881 | 2 |
| #4861 | 2 |
| #2911 | 3 |