Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #20260507 | C2 | semidirect |
| 5. #20260506 | C2 | semidirect |
| 6. #20260505 | C2 | semidirect |
| 7. #344×C97 | C2 | semidirect |
| 90. C97 | #1829 | semidirect |
| 97. #344 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261209 | 2 |
| C2×#15690726 | 2 |
| #20260507 | 2 |
| #20260506 | 2 |
| #20260505 | 2 |
| #344×C97 | 2 |
| #1829 | 97 |