Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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. #29508200 | C2 | semidirect |
| 3. #29507723 | C2 | semidirect |
| 4. #29507619 | C2 | semidirect |
| 5. #29507485 | C2 | semidirect |
| 6. #29507477 | C2 | semidirect |
| 7. C2×#104×C241 | C2 | semidirect |
| 10. #21440667 | C4 | semidirect |
| 34. C2×D964 | C2×C4 | semidirect |
| 40. #16838754 | C2×C4 | semidirect |
| 85. Q8×C241 | C22⋊C4 | semidirect |
| 89. D4×C241 | C22⋊C4 | semidirect |
| 132. C241 | #1883 | semidirect |
| 136. C2×#104 | 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 |
| #29508200 | 2 |
| #29507723 | 2 |
| #29507619 | 2 |
| #29507485 | 2 |
| #29507477 | 2 |
| C2×#104×C241 | 2 |
| #1883 | 241 |