Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. #22612180 | C2 | semidirect |
| 2. #22612008 | C2 | semidirect |
| 3. #22612004 | C2 | semidirect |
| 4. #22611767 | C2 | semidirect |
| 5. #22608006 | C2 | semidirect |
| 6. #22607967 | C2 | semidirect |
| 7. C73×#1357 | C2 | semidirect |
| 117. #1357 | D73 | semidirect |
| 118. C73 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612180 | 2 |
| #22612008 | 2 |
| #22612004 | 2 |
| #22611767 | 2 |
| #22608006 | 2 |
| #22607967 | 2 |
| C73×#1357 | 2 |
| #12436 | 73 |