Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #22577810 | C2 | semidirect |
| 4. #22577808 | C2 | semidirect |
| 5. #22577806 | C2 | semidirect |
| 6. #22577799 | C2 | semidirect |
| 9. #498×C137 | C2 | semidirect |
| 43. #14555493 | Q8 | semidirect |
| 79. #11764040 | C2×Q8 | semidirect |
| 87. C8×C137 | C2×Q8 | semidirect |
| 106. C137 | #3165 | semidirect |
| 114. #498 | D137 | semidirect |
| 194. C8 | Q8×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577958 | 2 |
| C4⋊Q8×D137 | 2 |
| #22577810 | 2 |
| #22577808 | 2 |
| #22577806 | 2 |
| #22577799 | 2 |
| #22577442 | 2 |
| C4×#14555493 | 2 |
| #498×C137 | 2 |
| #3165 | 137 |