Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22612111 | C2 | semidirect |
| 3. #22611420 | C2 | semidirect |
| 4. #22607941 | C2 | semidirect |
| 5. #22607940 | C2 | semidirect |
| 6. #22607870 | C2 | semidirect |
| 7. C73×#2232 | C2 | semidirect |
| 166. #2232 | D73 | semidirect |
| 171. C73 | #12288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621237 | 2 |
| #22612111 | 2 |
| #22611420 | 2 |
| #22607941 | 2 |
| #22607940 | 2 |
| #22607870 | 2 |
| C73×#2232 | 2 |
| #12288 | 73 |