Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
138 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 47 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. #20261136 | C2 | semidirect |
| 3. #20260539 | C2 | semidirect |
| 6. C16×Dic97 | C2 | semidirect |
| 7. #358×C97 | C2 | semidirect |
| 67. C97 | #2242 | semidirect |
| 71. #358 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261136 | 2 |
| #20261120 | 2 |
| #20260539 | 2 |
| #20260537 | 2 |
| #20260535 | 2 |
| C16×Dic97 | 2 |
| #358×C97 | 2 |
| #2242 | 97 |