Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
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. #30657503 | C2 | semidirect |
| 3. #30656719 | C2 | semidirect |
| 4. C2×#22551509 | C2 | semidirect |
| 5. #30656509 | C2 | semidirect |
| 6. #30656508 | C2 | semidirect |
| 7. C2×#100×C257 | C2 | semidirect |
| 38. #16861602 | D4 | semidirect |
| 58. M16×C257 | D4 | semidirect |
| 114. C257 | #1914 | semidirect |
| 120. C2×#100 | D257 | semidirect |
| 166. M16 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657503 | 2 |
| #30657304 | 2 |
| #30656719 | 2 |
| C2×#22551509 | 2 |
| #30656509 | 2 |
| #30656508 | 2 |
| C2×#100×C257 | 2 |
| #1914 | 257 |