Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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×#15690840 | C2 | semidirect |
| 2. #20261306 | C2 | semidirect |
| 3. #20260752 | C2 | semidirect |
| 4. #20260745 | C2 | semidirect |
| 5. #20260709 | C2 | semidirect |
| 6. #20260506 | C2 | semidirect |
| 137. C97 | #2009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| #20261306 | 2 |
| #20260752 | 2 |
| #20260745 | 2 |
| #20260709 | 2 |
| #20260506 | 2 |
| #575×C97 | 2 |
| #2009 | 97 |