Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22611704 | C2 | semidirect |
| 3. C2×#17988409 | C2 | semidirect |
| 6. #22608032 | C2 | semidirect |
| 7. C73×#1386 | C2 | semidirect |
| 21. #17988372 | C4 | semidirect |
| 43. C2×#11924003 | C2×C4 | semidirect |
| 56. M32×C73 | C2×C4 | semidirect |
| 158. #1386 | D73 | semidirect |
| 160. C73 | #12934 | semidirect |
| 200. M32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618522 | 2 |
| #22611704 | 2 |
| C2×#17988409 | 2 |
| #22611560 | 2 |
| #22609982 | 2 |
| #22608032 | 2 |
| C73×#1386 | 2 |
| #12934 | 73 |