Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
548 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #22609969 | C2 | semidirect |
| 3. #22608446 | C2 | semidirect |
| 4. #22608290 | C2 | semidirect |
| 5. C8×C22⋊C4×C73 | C2 | semidirect |
| 6. C22×D584 | C4 | semidirect |
| 13. C2×#14556525 | C4 | semidirect |
| 14. C2×#14556513 | C4 | semidirect |
| 173. C8×C22⋊C4 | D73 | semidirect |
| 176. C73 | #9815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988823 | 2 |
| #22609969 | 2 |
| #22608446 | 2 |
| #22608290 | 2 |
| C8×C22⋊C4×C73 | 2 |
| #9815 | 73 |