Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22578169 | C2 | semidirect |
| 3. #22577385 | C2 | semidirect |
| 4. C2×#17984005 | C2 | semidirect |
| 5. #22577175 | C2 | semidirect |
| 6. #22577174 | C2 | semidirect |
| 7. C2×#100×C137 | C2 | semidirect |
| 38. #14555494 | D4 | semidirect |
| 58. M16×C137 | D4 | semidirect |
| 114. C137 | #1914 | semidirect |
| 120. C2×#100 | D137 | semidirect |
| 166. M16 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578169 | 2 |
| #22577970 | 2 |
| #22577385 | 2 |
| C2×#17984005 | 2 |
| #22577175 | 2 |
| #22577174 | 2 |
| C2×#100×C137 | 2 |
| #1914 | 137 |