Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22611728 | C2 | semidirect |
| 3. #22608688 | C2 | semidirect |
| 4. #22607893 | C2 | semidirect |
| 5. #22607892 | C2 | semidirect |
| 6. #22607891 | C2 | semidirect |
| 7. C73×#1331 | C2 | semidirect |
| 21. C4×#11924003 | C22 | semidirect |
| 22. #17988340 | C22 | semidirect |
| 25. C4×C16×C73 | C22 | semidirect |
| 26. #335×C73 | C22 | semidirect |
| 77. D584 | M16 | semidirect |
| 98. D8×C73 | M16 | semidirect |
| 178. #1331 | D73 | semidirect |
| 179. C73 | #11657 | semidirect |
| 195. C4×C16 | C2×D73 | semidirect |
| 198. #335 | C2×D73 | semidirect |
| 254. D8 | #11924011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D73 | 2 |
| #22611728 | 2 |
| #22608688 | 2 |
| #22607893 | 2 |
| #22607892 | 2 |
| #22607891 | 2 |
| C73×#1331 | 2 |
| #11657 | 73 |