Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
954 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22624345 | C2 | semidirect |
| 2. #22621319 | C2 | semidirect |
| 4. #22609072 | C2 | semidirect |
| 5. #22609053 | C2 | semidirect |
| 6. #22609010 | C2 | semidirect |
| 7. #22608991 | C2 | semidirect |
| 8. #22608385 | C2 | semidirect |
| 9. C73×#1560 | C2 | semidirect |
| 198. #1560 | D73 | semidirect |
| 200. C73 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624345 | 2 |
| #22621319 | 2 |
| #22620357 | 2 |
| #22609072 | 2 |
| #22609053 | 2 |
| #22609010 | 2 |
| #22608991 | 2 |
| #22608385 | 2 |
| C73×#1560 | 2 |
| #18688 | 73 |