Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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. #13092619 | C2 | direct (N × H) |
| 4. C2×C4⋊(C23⋊C8) | C2 | semidirect |
| 5. C2×#10625017 | C2 | semidirect |
| 6. C2×C23×C4⋊Q8 | C2 | semidirect |
| 11. C23×C4⋊Q8 | C22 | semidirect |
| 22. #10625017 | C22 | semidirect |
| 23. C4⋊(C23⋊C8) | C22 | semidirect |
| 61. C2×C4×C23 | SD16 | semidirect |
| 87. C4×C23 | C2×SD16 | semidirect |
| 92. C2×C4⋊Q8 | D23 | semidirect |
| 97. C2×C23 | #461 | semidirect |
| 109. C4⋊Q8 | C2×D23 | semidirect |
| 119. C23 | C2×#461 | semidirect |
| 163. C2×C4 | #67274 | semidirect |
| 183. C4 | C2×#67274 | semidirect |
| 187. C2 | #13092619 | 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×C4×D92 | 2 |
| #13092619 | 2 |
| C2×C4⋊(C23⋊C8) | 2 |
| C2×#10625017 | 2 |
| C2×C23×C4⋊Q8 | 2 |
| C2×#461 | 23 |