Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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. #31771013 | C2 | direct (N × H) |
| 35. C2×#14524130 | Q8 | semidirect |
| 49. C2×C8×C269 | Q8 | semidirect |
| 64. #14524130 | C2×Q8 | semidirect |
| 74. C8×C269 | C2×Q8 | semidirect |
| 88. C2×C269 | #501 | semidirect |
| 92. C269 | C2×#501 | semidirect |
| 133. C2×C8 | Dic538 | semidirect |
| 167. C8 | C2×Dic538 | semidirect |
| 181. C2 | #31771013 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575452 | 2 |
| C2×#22575444 | 2 |
| #31771013 | 2 |
| C2×#22575386 | 2 |
| C2×#22575385 | 2 |
| C2×#22575384 | 2 |
| C2×#22575363 | 2 |
| C2×#107×C269 | 2 |
| C2×#501 | 269 |