Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
812 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#67274 | C2 | semidirect |
| 2. C22×#67272 | C2 | semidirect |
| 3. C2×#10625101 | C2 | semidirect |
| 4. #13092562 | C2 | direct (N × H) |
| 5. C2×#10625017 | C2 | semidirect |
| 6. C2×#10625014 | C2 | semidirect |
| 7. C2×C22⋊(C23⋊C8) | C2 | semidirect |
| 8. C22×#41×C23 | C2 | semidirect |
| 12. C2×#41×C23 | C22 | semidirect |
| 21. C2×#67274 | C22 | semidirect |
| 23. C2×#67272 | C22 | semidirect |
| 25. #10625101 | C22 | semidirect |
| 30. #10625017 | C22 | semidirect |
| 31. #10625014 | C22 | semidirect |
| 32. C22⋊(C23⋊C8) | C22 | semidirect |
| 41. C2×Q8×C23 | D4 | semidirect |
| 47. C2×D4×C23 | D4 | semidirect |
| 89. Q8×C23 | C2×D4 | semidirect |
| 93. D4×C23 | C2×D4 | semidirect |
| 137. C22×#41 | D23 | semidirect |
| 147. C2×C23 | #449 | semidirect |
| 155. C2×#41 | C2×D23 | semidirect |
| 176. C23 | C2×#449 | semidirect |
| 185. C2×Q8 | C22⋊D23 | semidirect |
| 197. C2×D4 | C22⋊D23 | semidirect |
| 233. Q8 | C2×C22⋊D23 | semidirect |
| 241. D4 | C2×C22⋊D23 | semidirect |
| 283. C2 | #13092562 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67274 | 2 |
| C22×#67272 | 2 |
| C2×#10625101 | 2 |
| #13092562 | 2 |
| C2×#10625017 | 2 |
| C2×#10625014 | 2 |
| C2×C22⋊(C23⋊C8) | 2 |
| C22×#41×C23 | 2 |
| C2×#449 | 23 |