Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 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. #31774192 | C2 | semidirect |
| 4. #31774107 | C2 | semidirect |
| 6. C4×#16864644 | C2 | semidirect |
| 78. C2×C4×C271 | Q16 | semidirect |
| 103. C271 | #3104 | semidirect |
| 181. C2×C4 | #16864644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| #31774232 | 2 |
| #31774192 | 2 |
| #31774107 | 2 |
| #31774053 | 2 |
| C4×#16864644 | 2 |
| #31773950 | 2 |
| C2×C4×Q8×C271 | 2 |
| #3104 | 271 |