Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×Q8×Dic23 | C2 | semidirect |
| 4. #13092502 | C2 | direct (N × H) |
| 5. C2×#10624990 | C2 | semidirect |
| 7. C2×C8×Dic23 | C2 | semidirect |
| 8. C2×C23×#103 | C2 | semidirect |
| 15. Q8×Dic23 | C22 | semidirect |
| 16. C2×#67274 | C4 | semidirect |
| 26. C23×#103 | C22 | semidirect |
| 28. C8×Dic23 | C22 | semidirect |
| 29. #10624990 | C22 | semidirect |
| 33. C2×Q8×C23 | C2×C4 | semidirect |
| 51. #67274 | C2×C4 | semidirect |
| 59. C2×C23⋊C8 | C2×C4 | semidirect |
| 68. Q8×C23 | C22×C4 | semidirect |
| 80. C2×Dic23 | SD16 | semidirect |
| 88. C23⋊C8 | C22×C4 | semidirect |
| 105. Dic23 | C2×SD16 | semidirect |
| 111. C2×#103 | D23 | semidirect |
| 114. C2×C23 | C4×SD16 | semidirect |
| 137. #103 | C2×D23 | semidirect |
| 140. C23 | C2×C4×SD16 | semidirect |
| 144. C2×Q8 | C4×D23 | semidirect |
| 179. Q8 | C2×C4×D23 | semidirect |
| 217. C2 | #13092502 | 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×Q8×Dic23 | 2 |
| C2×#10625064 | 2 |
| #13092502 | 2 |
| C2×#10624990 | 2 |
| C2×#10625003 | 2 |
| C2×C8×Dic23 | 2 |
| C2×C23×#103 | 2 |
| C2×C4×SD16 | 23 |