Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#17988401 | C2 | semidirect |
| 3. C2×#17988400 | C2 | semidirect |
| 4. #22611646 | C2 | semidirect |
| 5. #22610680 | C2 | semidirect |
| 6. #22608012 | C2 | semidirect |
| 7. C73×#2140 | C2 | semidirect |
| 61. #107×C73 | D4 | semidirect |
| 171. #2140 | D73 | semidirect |
| 174. C73 | #13413 | semidirect |
| 225. #107 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988962 | 2 |
| C2×#17988401 | 2 |
| C2×#17988400 | 2 |
| #22611646 | 2 |
| #22610680 | 2 |
| #22608012 | 2 |
| C73×#2140 | 2 |
| #13413 | 73 |