Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #22607995 | C2 | semidirect |
| 4. #22607980 | C2 | semidirect |
| 5. C73×#1713 | C2 | semidirect |
| 70. C8×C73 | SD32 | semidirect |
| 90. #1713 | D73 | semidirect |
| 94. C73 | #12493 | semidirect |
| 160. C8 | #14556534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611973 | 2 |
| #22608817 | 2 |
| #22607995 | 2 |
| #22607980 | 2 |
| C73×#1713 | 2 |
| #12493 | 73 |