Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #22610864 | C2 | semidirect |
| 2. #22608717 | C2 | semidirect |
| 3. #22608626 | C2 | semidirect |
| 4. #22608426 | C2 | semidirect |
| 5. #22608283 | C2 | semidirect |
| 6. #22607788 | C2 | semidirect |
| 201. C73 | #10508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610864 | 2 |
| #22608717 | 2 |
| #22608626 | 2 |
| #22608426 | 2 |
| #22608283 | 2 |
| #22607788 | 2 |
| C73×#3213 | 2 |
| #10508 | 73 |