Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22618731 | C2 | semidirect |
| 3. C2×#17988396 | C2 | semidirect |
| 4. #22611646 | C2 | semidirect |
| 5. #22610805 | C2 | semidirect |
| 6. #22608014 | C2 | semidirect |
| 7. C73×#1386 | C2 | semidirect |
| 12. #17989025 | C4 | semidirect |
| 41. C2×D584 | C2×C4 | semidirect |
| 65. M32×C73 | C2×C4 | semidirect |
| 89. Dic292 | C22⋊C4 | semidirect |
| 97. D584 | C22⋊C4 | semidirect |
| 190. #1386 | D73 | semidirect |
| 192. C73 | #13025 | semidirect |
| 244. M32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989025 | 2 |
| #22618731 | 2 |
| C2×#17988396 | 2 |
| #22611646 | 2 |
| #22610805 | 2 |
| #22608014 | 2 |
| C73×#1386 | 2 |
| #13025 | 73 |