Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 144 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 |
|---|---|---|
| 1. #20261153 | C2 | semidirect |
| 3. #20260520 | C2 | semidirect |
| 4. #20260511 | C2 | semidirect |
| 5. #364×C97 | C2 | semidirect |
| 50. C97 | #2171 | semidirect |
| 53. #364 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261153 | 2 |
| #20260853 | 2 |
| #20260520 | 2 |
| #20260511 | 2 |
| #364×C97 | 2 |
| #2171 | 97 |