Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
696 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 274 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. #22626028 | C2 | semidirect |
| 3. #22625984 | C2 | semidirect |
| 5. #22625863 | C2 | semidirect |
| 6. #22625858 | C2 | semidirect |
| 45. #126×C73 | C8 | semidirect |
| 73. C4⋊C4×C73 | C2×C8 | semidirect |
| 75. C42×C73 | C2×C8 | semidirect |
| 126. C73 | #23375 | semidirect |
| 150. #126 | #10596833 | semidirect |
| 186. C4⋊C4 | C2×#10596833 | semidirect |
| 194. C42 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626028 | 2 |
| #22626000 | 2 |
| #22625984 | 2 |
| #22625874 | 2 |
| #22625863 | 2 |
| #22625858 | 2 |
| #126×Dic73 | 2 |
| #23375 | 73 |