Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
792 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
| 3. #13092556 | C2 | direct (N × H) |
| 4. C2×#10625017 | C2 | semidirect |
| 5. C2×C22⋊(C23⋊C8) | C2 | semidirect |
| 6. C23×Q8×C23 | C2 | semidirect |
| 11. C22×Q8×C23 | C22 | semidirect |
| 17. C2×#67274 | C22 | semidirect |
| 23. #10625017 | C22 | semidirect |
| 24. C22⋊(C23⋊C8) | C22 | semidirect |
| 33. C2×Q8×C23 | D4 | semidirect |
| 57. C23×C23 | SD16 | semidirect |
| 67. Q8×C23 | C2×D4 | semidirect |
| 90. C22×C23 | C2×SD16 | semidirect |
| 102. C23×Q8 | D23 | semidirect |
| 109. C2×C23 | #448 | semidirect |
| 118. C22×Q8 | C2×D23 | semidirect |
| 132. C23 | C2×#448 | semidirect |
| 141. C2×Q8 | C22⋊D23 | semidirect |
| 169. C23 | #67274 | semidirect |
| 175. Q8 | C2×C22⋊D23 | semidirect |
| 200. C22 | C2×#67274 | semidirect |
| 211. C2 | #13092556 | 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 |
| C2×#10625101 | 2 |
| #13092556 | 2 |
| C2×#10625017 | 2 |
| C2×C22⋊(C23⋊C8) | 2 |
| C23×Q8×C23 | 2 |
| C2×#448 | 23 |