Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×#17984029 | C2 | semidirect |
| 2. C2×C16×D137 | C2 | semidirect |
| 3. #22577640 | C2 | semidirect |
| 4. #22577636 | C2 | semidirect |
| 5. #22577228 | C2 | semidirect |
| 6. #22577205 | C2 | semidirect |
| 7. #357×C137 | C2 | semidirect |
| 33. #14555485 | D4 | semidirect |
| 67. C2×D137 | D16 | semidirect |
| 79. C137 | #2215 | semidirect |
| 87. #357 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984029 | 2 |
| C2×C16×D137 | 2 |
| #22577640 | 2 |
| #22577636 | 2 |
| #22577228 | 2 |
| #22577205 | 2 |
| #357×C137 | 2 |
| #2215 | 137 |