Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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. C4×#14556526 | C2 | semidirect |
| 3. #22608523 | C2 | semidirect |
| 4. #22608522 | C2 | semidirect |
| 5. #22608347 | C2 | semidirect |
| 6. #22608221 | C2 | semidirect |
| 7. C73×#1484 | C2 | semidirect |
| 189. #1484 | D73 | semidirect |
| 191. C73 | #9726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620506 | 2 |
| C4×#14556526 | 2 |
| #22608523 | 2 |
| #22608522 | 2 |
| #22608347 | 2 |
| #22608221 | 2 |
| C73×#1484 | 2 |
| #9726 | 73 |