Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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. C22×D1168 | C2 | semidirect |
| 2. C22×#14556530 | C2 | semidirect |
| 3. C2×#17988824 | C2 | semidirect |
| 4. #22612035 | C2 | direct (N × H) |
| 5. C2×#17988387 | C2 | semidirect |
| 6. C2×#367×C73 | C2 | semidirect |
| 11. C2×D1168 | C22 | semidirect |
| 13. C2×#14556530 | C22 | semidirect |
| 16. #17988824 | C22 | semidirect |
| 18. #17988387 | C22 | semidirect |
| 21. #367×C73 | C22 | semidirect |
| 44. C2×C16×C73 | D4 | semidirect |
| 79. C16×C73 | C2×D4 | semidirect |
| 123. C2×C73 | #2218 | semidirect |
| 132. C2×#367 | D73 | semidirect |
| 134. C73 | C2×#2218 | semidirect |
| 148. #367 | C2×D73 | semidirect |
| 171. C2×C16 | D292 | semidirect |
| 207. C16 | C2×D292 | semidirect |
| 252. C2 | #22612035 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1168 | 2 |
| C22×#14556530 | 2 |
| C2×#17988824 | 2 |
| #22612035 | 2 |
| C2×#17988387 | 2 |
| C2×#367×C73 | 2 |
| C2×#2218 | 73 |