Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#17988426 | C2 | semidirect |
| 2. C2×#17988420 | C2 | semidirect |
| 3. #22612023 | C2 | semidirect |
| 5. #22608111 | C2 | semidirect |
| 6. #22608108 | C2 | semidirect |
| 7. C73×#1423 | C2 | semidirect |
| 39. C32×C73 | D4 | semidirect |
| 100. #1423 | D73 | semidirect |
| 103. C73 | #13699 | semidirect |
| 135. C32 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988426 | 2 |
| C2×#17988420 | 2 |
| #22612023 | 2 |
| #22612018 | 2 |
| #22608111 | 2 |
| #22608108 | 2 |
| C73×#1423 | 2 |
| #13699 | 73 |