Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 1. #19128408 | C2 | semidirect |
| 3. #19128099 | C2 | semidirect |
| 4. #19128032 | C2 | semidirect |
| 5. #19128020 | C2 | semidirect |
| 6. #19127992 | C2 | semidirect |
| 7. #19127987 | C2 | semidirect |
| 8. #19127930 | C2 | semidirect |
| 9. C4×#13050579 | C2 | semidirect |
| 10. C2×#14581724 | C2 | semidirect |
| 11. C8×D4×C83 | C2 | semidirect |
| 76. D4×C83 | SD16 | semidirect |
| 100. C8×C83 | #41 | semidirect |
| 124. C83 | #3335 | semidirect |
| 134. C8×D4 | D83 | semidirect |
| 207. D4 | #13050579 | semidirect |
| 224. C8 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128408 | 2 |
| #19128355 | 2 |
| #19128099 | 2 |
| #19128032 | 2 |
| #19128020 | 2 |
| #19127992 | 2 |
| #19127987 | 2 |
| #19127930 | 2 |
| C4×#13050579 | 2 |
| C2×#14581724 | 2 |
| C8×D4×C83 | 2 |
| #3335 | 83 |