Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22611685 | C2 | semidirect |
| 3. #346×D73 | C2 | semidirect |
| 4. #22607890 | C2 | semidirect |
| 5. #22607889 | C2 | semidirect |
| 6. #22607888 | C2 | semidirect |
| 7. C73×#1330 | C2 | semidirect |
| 174. #1330 | D73 | semidirect |
| 175. C73 | #11588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618640 | 2 |
| #22611685 | 2 |
| #346×D73 | 2 |
| #22607890 | 2 |
| #22607889 | 2 |
| #22607888 | 2 |
| C73×#1330 | 2 |
| #11588 | 73 |