Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
570 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22621056 | C2 | semidirect |
| 2. #22620853 | C2 | semidirect |
| 3. #22610904 | C2 | semidirect |
| 4. #22608491 | C2 | semidirect |
| 5. #22608491 | C2 | semidirect |
| 6. #22607776 | C2 | semidirect |
| 115. C2×C8×C73 | SD16 | semidirect |
| 203. C73 | #10221 | semidirect |
| 306. C2×C8 | #11924016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621056 | 2 |
| #22620853 | 2 |
| #22610904 | 2 |
| #22608491 | 2 |
| #22607776 | 2 |
| C73×#3150 | 2 |
| #10221 | 73 |