Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 584 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 |
| 3. #13092617 | C2 | direct (N × H) |
| 4. C2×C4⋊(C23⋊C8) | C2 | semidirect |
| 5. C2×#10624991 | C2 | semidirect |
| 6. C2×C4×Q8×C23 | C2 | semidirect |
| 12. C4×Q8×C23 | C22 | semidirect |
| 18. C2×#67274 | C22 | semidirect |
| 22. #10624991 | C22 | semidirect |
| 23. C4⋊(C23⋊C8) | C22 | semidirect |
| 27. C2×Q8×C23 | D4 | semidirect |
| 58. Q8×C23 | C2×D4 | semidirect |
| 64. C2×C4×C23 | SD16 | semidirect |
| 90. C4×C23 | C2×SD16 | semidirect |
| 95. C2×C4×Q8 | D23 | semidirect |
| 99. C2×C23 | #460 | semidirect |
| 114. C4×Q8 | C2×D23 | semidirect |
| 121. C23 | C2×#460 | semidirect |
| 125. C2×Q8 | D92 | semidirect |
| 156. Q8 | C2×D92 | semidirect |
| 167. C2×C4 | #67274 | semidirect |
| 187. C4 | C2×#67274 | semidirect |
| 191. C2 | #13092617 | 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×#10625045 | 2 |
| #13092617 | 2 |
| C2×C4⋊(C23⋊C8) | 2 |
| C2×#10624991 | 2 |
| C2×C4×Q8×C23 | 2 |
| C2×#460 | 23 |