Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 278 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. #22623081 | C2 | semidirect |
| 2. #22612243 | C2 | semidirect |
| 3. C2×#17988426 | C2 | semidirect |
| 4. #22612052 | C2 | semidirect |
| 5. #22608123 | C2 | semidirect |
| 6. #22608072 | C2 | semidirect |
| 7. C73×#1417 | C2 | semidirect |
| 124. #1417 | D73 | semidirect |
| 126. C73 | #13670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623081 | 2 |
| #22612243 | 2 |
| C2×#17988426 | 2 |
| #22612052 | 2 |
| #22608123 | 2 |
| #22608072 | 2 |
| C73×#1417 | 2 |
| #13670 | 73 |