Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22578110 | C2 | semidirect |
| 2. #22578074 | C2 | semidirect |
| 3. #22577766 | C2 | semidirect |
| 4. #22577750 | C2 | semidirect |
| 5. #22577706 | C2 | semidirect |
| 6. #22577693 | C2 | semidirect |
| 7. #22577598 | C2 | semidirect |
| 8. #22577596 | C2 | semidirect |
| 9. #22577533 | C2 | semidirect |
| 10. #22577512 | C2 | semidirect |
| 11. C4×D8×C137 | C2 | semidirect |
| 94. D4×C137 | #41 | semidirect |
| 129. C137 | #3366 | semidirect |
| 141. C4×D8 | D137 | semidirect |
| 218. D4 | #14555510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578110 | 2 |
| #22578074 | 2 |
| #22577766 | 2 |
| #22577750 | 2 |
| #22577706 | 2 |
| #22577693 | 2 |
| #22577598 | 2 |
| #22577596 | 2 |
| #22577533 | 2 |
| #22577512 | 2 |
| C4×D8×C137 | 2 |
| #3366 | 137 |