Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22578075 | C2 | semidirect |
| 2. #22577751 | C2 | semidirect |
| 3. #22577680 | C2 | semidirect |
| 4. #22577598 | C2 | semidirect |
| 5. Q8×#11764040 | C2 | semidirect |
| 6. C4×#14555495 | C2 | semidirect |
| 7. D4×Q8×C137 | C2 | semidirect |
| 55. Q8×C137 | D8 | semidirect |
| 57. D4×C137 | #41 | semidirect |
| 81. C137 | #3358 | semidirect |
| 84. D4×Q8 | D137 | semidirect |
| 129. Q8 | #14555495 | semidirect |
| 135. D4 | #14555511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578075 | 2 |
| #22577751 | 2 |
| #22577680 | 2 |
| #22577598 | 2 |
| Q8×#11764040 | 2 |
| C4×#14555495 | 2 |
| D4×Q8×C137 | 2 |
| #3358 | 137 |