Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#15690755 | C2 | semidirect |
| 2. #20261151 | C2 | semidirect |
| 3. #20261011 | C2 | semidirect |
| 5. #20260550 | C2 | semidirect |
| 6. #20260547 | C2 | semidirect |
| 7. #368×C97 | C2 | semidirect |
| 72. C97 | #2223 | semidirect |
| 77. #368 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690755 | 2 |
| #20261151 | 2 |
| #20261011 | 2 |
| #20261006 | 2 |
| #20260550 | 2 |
| #20260547 | 2 |
| #368×C97 | 2 |
| #2223 | 97 |