Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D404 | C2 | semidirect |
| 2. #20265536 | C2 | semidirect |
| 3. #20265527 | C2 | semidirect |
| 4. #20265472 | C2 | semidirect |
| 5. #20265457 | C2 | semidirect |
| 7. #20265379 | C2 | semidirect |
| 8. #20265308 | C2 | semidirect |
| 9. #20265275 | C2 | semidirect |
| 11. #556×C101 | C2 | semidirect |
| 123. C101 | #3367 | semidirect |
| 124. #556 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D404 | 2 |
| #20265536 | 2 |
| #20265527 | 2 |
| #20265472 | 2 |
| #20265457 | 2 |
| #20265389 | 2 |
| #20265379 | 2 |
| #20265308 | 2 |
| #20265275 | 2 |
| C4×#13108059 | 2 |
| #556×C101 | 2 |
| #3367 | 101 |