Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22611717 | C2 | semidirect |
| 4. #22610714 | C2 | semidirect |
| 5. #22608027 | C2 | semidirect |
| 6. #22608019 | C2 | semidirect |
| 20. #17988400 | C4 | semidirect |
| 36. #14556531 | C2×C4 | semidirect |
| 39. #14556527 | C2×C4 | semidirect |
| 167. C73 | #12940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618783 | 2 |
| #22611717 | 2 |
| C2×#17988400 | 2 |
| #22610714 | 2 |
| #22608027 | 2 |
| #22608019 | 2 |
| C2×#357×C73 | 2 |
| #12940 | 73 |