Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #22608360 | C2 | semidirect |
| 5. #22607828 | C2 | semidirect |
| 6. #22607776 | C2 | semidirect |
| 7. C73×#1985 | C2 | semidirect |
| 109. C2×C8×C73 | SD16 | semidirect |
| 188. #1985 | D73 | semidirect |
| 193. C73 | #9047 | semidirect |
| 291. C2×C8 | #11924015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619962 | 2 |
| #22618650 | 2 |
| #22608581 | 2 |
| #22608360 | 2 |
| #22607828 | 2 |
| #22607776 | 2 |
| C73×#1985 | 2 |
| #9047 | 73 |