Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
348 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22610924 | C2 | semidirect |
| 3. #22608699 | C2 | semidirect |
| 5. #22608534 | C2 | semidirect |
| 7. C73×#1291 | C2 | semidirect |
| 172. #1291 | D73 | semidirect |
| 173. C73 | #10497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621123 | 2 |
| #22610924 | 2 |
| #22608699 | 2 |
| #22608654 | 2 |
| #22608534 | 2 |
| #22608522 | 2 |
| C73×#1291 | 2 |
| #10497 | 73 |