Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
| 35. #14556530 | C8 | semidirect |
| 61. #11924003 | C2×C8 | semidirect |
| 66. C16×C73 | C2×C8 | semidirect |
| 112. C73 | #12009 | semidirect |
| 171. C16 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625481 | 2 |
| #22625476 | 2 |
| #22624965 | 2 |
| #22624964 | 2 |
| #22624963 | 2 |
| #22624962 | 2 |
| #22611524 | 2 |
| #12009 | 73 |