Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #22609958 | C2 | semidirect |
| 4. #22609709 | C2 | semidirect |
| 5. #22608503 | C2 | semidirect |
| 7. C73×#1996 | C2 | semidirect |
| 8. C22×#11924015 | C4 | semidirect |
| 16. C2×#14556522 | C4 | semidirect |
| 17. C2×#14556515 | C4 | semidirect |
| 18. C2×#14556511 | C4 | semidirect |
| 194. #10596831 | #99 | semidirect |
| 233. #1996 | D73 | semidirect |
| 239. C73 | #9786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988818 | 2 |
| #22610767 | 2 |
| #22609958 | 2 |
| #22609709 | 2 |
| #22608503 | 2 |
| #22608498 | 2 |
| C73×#1996 | 2 |
| #9786 | 73 |