Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×#21440569 | C2 | semidirect |
| 3. #29507721 | C2 | semidirect |
| 4. #29507618 | C2 | semidirect |
| 5. #29507486 | C2 | semidirect |
| 6. #29507476 | C2 | semidirect |
| 7. #520×C241 | C2 | semidirect |
| 10. #21440667 | C4 | semidirect |
| 34. C2×D964 | C2×C4 | semidirect |
| 41. #16838754 | C2×C4 | semidirect |
| 84. Q8×C241 | C22⋊C4 | semidirect |
| 88. D4×C241 | C22⋊C4 | semidirect |
| 132. C241 | #1883 | semidirect |
| 135. #520 | D241 | semidirect |
| 208. Q8 | #16838747 | semidirect |
| 216. D4 | #16838747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440667 | 2 |
| C2×#21440569 | 2 |
| #29507721 | 2 |
| #29507618 | 2 |
| #29507486 | 2 |
| #29507476 | 2 |
| #520×C241 | 2 |
| #1883 | 241 |