Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
798 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 211 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. #22620491 | C2 | semidirect |
| 3. #22609565 | C2 | semidirect |
| 4. #22609560 | C2 | semidirect |
| 5. #22609554 | C2 | semidirect |
| 6. C2×#17988308 | C2 | semidirect |
| 7. C73×#3160 | C2 | semidirect |
| 75. C2×C8×C73 | SD16 | semidirect |
| 122. #3160 | D73 | semidirect |
| 128. C73 | #19608 | semidirect |
| 194. C2×C8 | #11924015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620491 | 2 |
| #22620359 | 2 |
| #22609565 | 2 |
| #22609560 | 2 |
| #22609554 | 2 |
| C2×#17988308 | 2 |
| C73×#3160 | 2 |
| #19608 | 73 |