Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
540 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 229 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. #29507616 | C2 | semidirect |
| 3. #29507610 | C2 | semidirect |
| 4. #29507580 | C2 | semidirect |
| 5. #29507577 | C2 | semidirect |
| 6. C4×C4⋊Dic241 | C2 | semidirect |
| 7. #29507563 | C2 | semidirect |
| 22. C4×D4×C241 | C4 | semidirect |
| 96. C241 | #2319 | semidirect |
| 108. C4×D4 | Dic241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29507620 | 2 |
| #29507616 | 2 |
| #29507610 | 2 |
| #29507580 | 2 |
| #29507577 | 2 |
| C4×C4⋊Dic241 | 2 |
| #29507563 | 2 |
| C2×C4×D4×C241 | 2 |
| #2319 | 241 |