Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 4. #22610714 | C2 | semidirect |
| 5. #22608026 | C2 | semidirect |
| 6. #22608021 | C2 | semidirect |
| 7. C73×#2159 | C2 | semidirect |
| 18. #17988401 | C4 | semidirect |
| 45. #14556527 | C2×C4 | semidirect |
| 56. M32×C73 | C2×C4 | semidirect |
| 161. #2159 | D73 | semidirect |
| 167. C73 | #12940 | semidirect |
| 205. M32 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618782 | 2 |
| C2×#17988401 | 2 |
| C2×#17988387 | 2 |
| #22610714 | 2 |
| #22608026 | 2 |
| #22608021 | 2 |
| C73×#2159 | 2 |
| #12940 | 73 |