Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1074 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22610395 | C2 | semidirect |
| 2. #22610229 | C2 | semidirect |
| 3. #22608291 | C2 | semidirect |
| 4. #22608269 | C2 | semidirect |
| 6. C22×#11924012 | C22 | semidirect |
| 8. #17988551 | C22 | semidirect |
| 10. C2×C22⋊#10596831 | C22 | semidirect |
| 161. C23×C73 | #100 | semidirect |
| 195. C2×C4×C73 | #100 | semidirect |
| 244. C73 | #8536 | semidirect |
| 400. C23 | #14556508 | semidirect |
| 434. C2×C4 | #14556508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610395 | 2 |
| #22610229 | 2 |
| #22608291 | 2 |
| #22608269 | 2 |
| C73×#3496 | 2 |
| #8536 | 73 |