Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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. #19127780 | C2 | semidirect |
| 3. #19127451 | C2 | semidirect |
| 4. D4⋊(C83⋊C8) | C2 | semidirect |
| 5. #19127428 | C2 | semidirect |
| 6. #19127423 | C2 | semidirect |
| 7. #436×C83 | C2 | semidirect |
| 63. C83⋊C8 | M16 | semidirect |
| 84. C83 | #1594 | semidirect |
| 87. #436 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13050575 | 2 |
| #19127780 | 2 |
| #19127451 | 2 |
| D4⋊(C83⋊C8) | 2 |
| #19127428 | 2 |
| #19127423 | 2 |
| #436×C83 | 2 |
| #1594 | 83 |