Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #13092458 | C2 | direct (N × H) |
| 5. C2×#10624989 | C2 | semidirect |
| 6. C2×#10624999 | C2 | semidirect |
| 7. C2×#10624990 | C2 | semidirect |
| 8. C2×C23×#107 | C2 | semidirect |
| 20. C2×#67262 | C4 | semidirect |
| 26. C23×#107 | C22 | semidirect |
| 27. #10624999 | C22 | semidirect |
| 28. #10624990 | C22 | semidirect |
| 29. #10624989 | C22 | semidirect |
| 43. C2×C8×C23 | C2×C4 | semidirect |
| 56. C2×C23⋊C8 | C2×C4 | semidirect |
| 58. #67262 | C2×C4 | semidirect |
| 82. C8×C23 | C22×C4 | semidirect |
| 83. C23⋊C8 | C22×C4 | semidirect |
| 106. C2×#107 | D23 | semidirect |
| 109. C2×C23 | #428 | semidirect |
| 132. #107 | C2×D23 | semidirect |
| 135. C23 | C2×#428 | semidirect |
| 152. C2×C8 | C4×D23 | semidirect |
| 189. C8 | C2×C4×D23 | semidirect |
| 207. C2 | #13092458 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67262 | 2 |
| C2×#10625063 | 2 |
| C2×C4⋊C4×D23 | 2 |
| #13092458 | 2 |
| C2×#10624989 | 2 |
| C2×#10624999 | 2 |
| C2×#10624990 | 2 |
| C2×C23×#107 | 2 |
| C2×#428 | 23 |