Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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. C2×#22575845 | C2 | semidirect |
| 2. C2×D541⋊C8 | C2 | semidirect |
| 3. C4⋊#16864520 | C2 | semidirect |
| 4. #31772685 | C2 | semidirect |
| 5. C22⋊#16864520 | C2 | semidirect |
| 6. #31772683 | C2 | semidirect |
| 24. #16864520 | D4 | semidirect |
| 43. C2×D541 | M16 | semidirect |
| 55. C541 | #435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575845 | 2 |
| C2×D541⋊C8 | 2 |
| C4⋊#16864520 | 2 |
| #31772685 | 2 |
| C22⋊#16864520 | 2 |
| #31772683 | 2 |
| #31772588 | 2 |
| #435 | 541 |