Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20265897 | C2 | semidirect |
| 2. D4×Dic202 | C2 | semidirect |
| 3. #20265535 | C2 | semidirect |
| 4. #20265528 | C2 | semidirect |
| 5. #20265471 | C2 | semidirect |
| 6. #20265457 | C2 | semidirect |
| 8. #20265382 | C2 | semidirect |
| 9. #20265307 | C2 | semidirect |
| 10. #20265274 | C2 | semidirect |
| 123. C101 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265897 | 2 |
| D4×Dic202 | 2 |
| #20265535 | 2 |
| #20265528 | 2 |
| #20265471 | 2 |
| #20265457 | 2 |
| #20265390 | 2 |
| #20265382 | 2 |
| #20265307 | 2 |
| #20265274 | 2 |
| C4×D8×C101 | 2 |
| #3367 | 101 |