Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
232 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 88 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. #22624957 | C2 | semidirect |
| 3. #22624956 | C2 | semidirect |
| 4. #22624955 | C2 | semidirect |
| 45. #11924003 | M16 | semidirect |
| 52. C16×C73 | M16 | semidirect |
| 85. C73 | #12020 | semidirect |
| 132. C16 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625485 | 2 |
| #22624957 | 2 |
| #22624956 | 2 |
| #22624955 | 2 |
| M32×Dic73 | 2 |
| #12020 | 73 |