Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
204 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 65 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×#17988425 | C2 | semidirect |
| 2. C22×#14556497 | C2 | semidirect |
| 3. #22612022 | C2 | semidirect |
| 4. #22608132 | C2 | semidirect |
| 5. #22608111 | C2 | semidirect |
| 6. #22608109 | C2 | semidirect |
| 28. #14556497 | D4 | semidirect |
| 82. C22×C73 | SD64 | semidirect |
| 103. C73 | #13696 | semidirect |
| 178. C22 | #17988425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988425 | 2 |
| C22×#14556497 | 2 |
| #22612022 | 2 |
| #22608132 | 2 |
| #22608111 | 2 |
| #22608109 | 2 |
| C73×#2215 | 2 |
| #13696 | 73 |