Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #22577883 | C2 | semidirect |
| 3. #22577747 | C2 | semidirect |
| 4. #22577740 | C2 | semidirect |
| 5. #22577729 | C2 | semidirect |
| 6. #22577718 | C2 | semidirect |
| 7. C2×#17984021 | C2 | semidirect |
| 8. #22577405 | C2 | semidirect |
| 9. #22577397 | C2 | semidirect |
| 10. #22577371 | C2 | semidirect |
| 11. #428×C137 | C2 | semidirect |
| 133. C137 | #3098 | semidirect |
| 141. #428 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577984 | 2 |
| #22577883 | 2 |
| #22577747 | 2 |
| #22577740 | 2 |
| #22577729 | 2 |
| #22577718 | 2 |
| C2×#17984021 | 2 |
| #22577405 | 2 |
| #22577397 | 2 |
| #22577371 | 2 |
| #428×C137 | 2 |
| #3098 | 137 |