Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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. #19127956 | C2 | semidirect |
| 4. #19127939 | C2 | semidirect |
| 5. #19127739 | C2 | semidirect |
| 6. #19127710 | C2 | semidirect |
| 7. C22×Q16×C83 | C2 | semidirect |
| 89. C83 | #3059 | semidirect |
| 90. C22×Q16 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581798 | 2 |
| #19128275 | 2 |
| #19127956 | 2 |
| #19127939 | 2 |
| #19127739 | 2 |
| #19127710 | 2 |
| C22×Q16×C83 | 2 |
| #3059 | 83 |