Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 18. #125×C97 | C4 | semidirect |
| 70. Dic97 | #125 | direct (N × H) |
| 77. C97 | C4×#125 | semidirect |
| 85. #125 | Dic97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260634 | 2 |
| #20260621 | 2 |
| #20260601 | 2 |
| C4⋊C4×Dic97 | 2 |
| C42×Dic97 | 2 |
| C2×#125×C97 | 2 |
| C4×#125 | 97 |