Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22626692 | C2 | semidirect |
| 3. #22626241 | C2 | semidirect |
| 5. #22624999 | C2 | semidirect |
| 6. #22624980 | C2 | semidirect |
| 24. C2×#14556537 | C4 | semidirect |
| 25. C2×#14556536 | C4 | semidirect |
| 26. C2×#14556534 | C4 | semidirect |
| 28. C2×Q32×C73 | C4 | semidirect |
| 189. C73 | #13034 | semidirect |
| 196. C2×Q32 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626692 | 2 |
| #22626253 | 2 |
| #22626241 | 2 |
| #22626090 | 2 |
| #22624999 | 2 |
| #22624980 | 2 |
| C2×#17989029 | 2 |
| #13034 | 73 |