Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. #22612004 | C2 | semidirect |
| 2. #22611769 | C2 | semidirect |
| 3. #22608007 | C2 | semidirect |
| 4. #22607968 | C2 | semidirect |
| 5. C73×#2246 | C2 | semidirect |
| 85. #2246 | D73 | semidirect |
| 90. C73 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612004 | 2 |
| #22611769 | 2 |
| #22608007 | 2 |
| #22607968 | 2 |
| C73×#2246 | 2 |
| #12436 | 73 |