Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
654 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 654 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 |
|---|---|---|
| 1. #22627071 | C2 | semidirect |
| 2. #22626932 | C2 | semidirect |
| 3. #22626930 | C2 | semidirect |
| 34. C2×#11924029 | C8 | semidirect |
| 36. C2×#11924028 | C8 | semidirect |
| 38. C2×#11924027 | C8 | semidirect |
| 46. C2×#41×C73 | C8 | semidirect |
| 208. C73 | #7597 | semidirect |
| 228. C2×#41 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| #22626932 | 2 |
| #22626930 | 2 |
| #22626392 | 2 |
| #7597 | 73 |