Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
502 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22610008 | C2 | semidirect |
| 3. #22607929 | C2 | semidirect |
| 4. C73×#1464 | C2 | semidirect |
| 5. C2×#14556588 | C4 | semidirect |
| 8. #17988504 | C4 | semidirect |
| 12. #17988453 | C4 | semidirect |
| 166. #1464 | D73 | semidirect |
| 168. C73 | #11800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615681 | 2 |
| #22610008 | 2 |
| #22607929 | 2 |
| C73×#1464 | 2 |
| #11800 | 73 |