Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22621059 | C2 | semidirect |
| 2. #22620883 | C2 | semidirect |
| 4. #22609588 | C2 | semidirect |
| 5. #22609573 | C2 | semidirect |
| 6. #22609566 | C2 | semidirect |
| 7. #22609534 | C2 | semidirect |
| 8. #22608228 | C2 | semidirect |
| 9. C73×#3139 | C2 | semidirect |
| 162. #3139 | D73 | semidirect |
| 168. C73 | #19724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621059 | 2 |
| #22620883 | 2 |
| #22620669 | 2 |
| #22609588 | 2 |
| #22609573 | 2 |
| #22609566 | 2 |
| #22609534 | 2 |
| #22608228 | 2 |
| C73×#3139 | 2 |
| #19724 | 73 |