Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
372 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22611550 | C2 | semidirect |
| 3. #22607881 | C2 | semidirect |
| 4. #22607869 | C2 | semidirect |
| 5. C73×#1321 | C2 | semidirect |
| 141. #1321 | D73 | semidirect |
| 142. C73 | #11485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618639 | 2 |
| #22611550 | 2 |
| #22607881 | 2 |
| #22607869 | 2 |
| C73×#1321 | 2 |
| #11485 | 73 |