Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C2×D3×C4⋊C4 | C2 | semidirect |
| 4. C2×C3×#102 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. C2×#816 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4771 | C2 | direct (N × H) |
| 15. C2×#237 | C4 | semidirect |
| 26. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 28. D3×C4⋊C4 | C22 | semidirect |
| 29. C3×#102 | C22 | semidirect |
| 30. #832 | C22 | semidirect |
| 31. #816 | C22 | semidirect |
| 32. #810 | C22 | semidirect |
| 40. C2×#102 | D3 | semidirect |
| 45. C2×C3×D4 | C2×C4 | semidirect |
| 58. #237 | C2×C4 | semidirect |
| 67. C2×Dic6 | C2×C4 | semidirect |
| 101. #102 | C2×D3 | semidirect |
| 113. C3×D4 | C22×C4 | semidirect |
| 134. Dic6 | C22×C4 | semidirect |
| 150. C2×D4 | C4×D3 | semidirect |
| 209. D4 | C2×C4×D3 | semidirect |
| 230. C2×C3 | #417 | semidirect |
| 254. C3 | C2×#417 | semidirect |
| 257. C2 | #4771 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#237 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C2×D3×C4⋊C4 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×#816 | 2 |
| C2×#810 | 2 |
| #4771 | 2 |
| C2×#417 | 3 |