Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22577886 | C2 | semidirect |
| 3. #22577745 | C2 | semidirect |
| 4. #22577739 | C2 | semidirect |
| 5. #22577728 | C2 | semidirect |
| 6. #22577717 | C2 | semidirect |
| 7. #22577445 | C2 | semidirect |
| 8. C2×#17984022 | C2 | semidirect |
| 9. #22577405 | C2 | semidirect |
| 10. #22577400 | C2 | semidirect |
| 11. #408×C137 | C2 | semidirect |
| 133. C137 | #3098 | semidirect |
| 145. #408 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577981 | 2 |
| #22577886 | 2 |
| #22577745 | 2 |
| #22577739 | 2 |
| #22577728 | 2 |
| #22577717 | 2 |
| #22577445 | 2 |
| C2×#17984022 | 2 |
| #22577405 | 2 |
| #22577400 | 2 |
| #408×C137 | 2 |
| #3098 | 137 |