Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
224 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #22624965 | C2 | semidirect |
| 4. #22624964 | C2 | semidirect |
| 5. #22624963 | C2 | semidirect |
| 6. #22624962 | C2 | semidirect |
| 59. #11924003 | M16 | semidirect |
| 66. C16×C73 | M16 | semidirect |
| 112. C73 | #12025 | semidirect |
| 171. C16 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625493 | 2 |
| #22625488 | 2 |
| #22624965 | 2 |
| #22624964 | 2 |
| #22624963 | 2 |
| #22624962 | 2 |
| M32×Dic73 | 2 |
| #12025 | 73 |