Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
12190 conjugacy classes of subgroups; only the 5451 normal subgroups are shown.
This group has 12190 conjugacy classes of subgroups — too many to draw. Only its 5451 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. C22×#66922 | C2 | direct (N × H) |
| 12. C2×#66922 | C22 | direct (N × H) |
| 15. C23×C4×C11 | Q8 | semidirect |
| 24. #66922 | C23 | direct (N × H) |
| 30. C22×C4×C11 | C2×Q8 | semidirect |
| 43. C23×C11 | C4⋊Q8 | semidirect |
| 48. C2×C4×C11 | C22×Q8 | semidirect |
| 62. C22×C11 | C2×C4⋊Q8 | semidirect |
| 67. C4×C11 | C23×Q8 | semidirect |
| 74. C23×C4 | Dic22 | semidirect |
| 81. C2×C11 | C22×C4⋊Q8 | semidirect |
| 91. C22×C4 | C2×Dic22 | semidirect |
| 97. C11 | C23×C4⋊Q8 | semidirect |
| 98. C23 | #66922 | direct (N × H) |
| 105. C2×C4 | C22×Dic22 | semidirect |
| 109. C22 | C2×#66922 | direct (N × H) |
| 114. C4 | C23×Dic22 | semidirect |
| 116. C2 | C22×#66922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic22 | 2 |
| C22×#66922 | 2 |
| C23×C4⋊Dic11 | 2 |
| C23×C42×C11 | 2 |
| C23×C4⋊Q8 | 11 |