Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
182 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22577482 | C2 | semidirect |
| 3. #22577153 | C2 | semidirect |
| 4. D4⋊#11764040 | C2 | semidirect |
| 5. #22577130 | C2 | semidirect |
| 6. #22577125 | C2 | semidirect |
| 7. C8×D4×C137 | C2 | semidirect |
| 54. D4×C137 | M16 | semidirect |
| 83. C137 | #1586 | semidirect |
| 87. C8×D4 | D137 | semidirect |
| 131. D4 | #14555493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14555495 | 2 |
| #22577482 | 2 |
| #22577153 | 2 |
| D4⋊#11764040 | 2 |
| #22577130 | 2 |
| #22577125 | 2 |
| C8×D4×C137 | 2 |
| #1586 | 137 |