Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
176 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 3. #22608130 | C2 | semidirect |
| 4. #22608113 | C2 | semidirect |
| 5. #22608111 | C2 | semidirect |
| 7. C73×#1423 | C2 | semidirect |
| 88. #1423 | D73 | semidirect |
| 92. C73 | #13715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612023 | 2 |
| #366×D73 | 2 |
| #22608130 | 2 |
| #22608113 | 2 |
| #22608111 | 2 |
| #22608068 | 2 |
| C73×#1423 | 2 |
| #13715 | 73 |