Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626593 | C2 | semidirect |
| 2. #22626246 | C2 | semidirect |
| 3. C2×#17989501 | C2 | semidirect |
| 4. #22626171 | C2 | semidirect |
| 5. #22625010 | C2 | semidirect |
| 6. #22624990 | C2 | semidirect |
| 231. C73 | #12995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626593 | 2 |
| #22626246 | 2 |
| C2×#17989501 | 2 |
| #22626171 | 2 |
| #22625010 | 2 |
| #22624990 | 2 |
| #22619649 | 2 |
| #12995 | 73 |