Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22618591 | C2 | semidirect |
| 3. #22610023 | C2 | semidirect |
| 6. #22607818 | C2 | semidirect |
| 7. C73×#1305 | C2 | semidirect |
| 17. #17988629 | C4 | semidirect |
| 18. #17988629 | C4 | semidirect |
| 20. #17988593 | C4 | semidirect |
| 21. #17988593 | C4 | semidirect |
| 228. #1305 | D73 | semidirect |
| 230. C73 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619872 | 2 |
| #22618591 | 2 |
| #22610023 | 2 |
| #22608498 | 2 |
| #22608292 | 2 |
| #22607818 | 2 |
| C73×#1305 | 2 |
| #9348 | 73 |