Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
732 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 216 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. #22625987 | C2 | semidirect |
| 3. #22625858 | C2 | semidirect |
| 4. #22625731 | C2 | semidirect |
| 6. C42×#10596833 | C2 | semidirect |
| 76. C42×C73 | M16 | semidirect |
| 101. #10596833 | #126 | semidirect |
| 127. C73 | #21666 | semidirect |
| 196. C42 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626001 | 2 |
| #22625987 | 2 |
| #22625858 | 2 |
| #22625731 | 2 |
| #22625673 | 2 |
| C42×#10596833 | 2 |
| #126×Dic73 | 2 |
| #21666 | 73 |