Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 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. #22623068 | C2 | semidirect |
| 2. #22612246 | C2 | semidirect |
| 3. C2×#17988422 | C2 | semidirect |
| 4. #22612052 | C2 | semidirect |
| 5. #22608114 | C2 | semidirect |
| 6. #22608074 | C2 | semidirect |
| 7. C73×#1419 | C2 | semidirect |
| 13. C2×D1168 | C22 | semidirect |
| 20. C2×#14556497 | C22 | semidirect |
| 23. M64×C73 | C22 | semidirect |
| 24. #368×C73 | C22 | semidirect |
| 126. #1419 | D73 | semidirect |
| 129. C73 | #13669 | semidirect |
| 143. M64 | C2×D73 | semidirect |
| 145. #368 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623068 | 2 |
| #22612246 | 2 |
| C2×#17988422 | 2 |
| #22612052 | 2 |
| #22608114 | 2 |
| #22608074 | 2 |
| C73×#1419 | 2 |
| #13669 | 73 |