Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #20260776 | C2 | semidirect |
| 4. #20260775 | C2 | semidirect |
| 5. #20260773 | C2 | semidirect |
| 6. #20260772 | C2 | semidirect |
| 7. #107×D97 | C2 | semidirect |
| 8. C2×#107×C97 | C2 | semidirect |
| 10. #15690816 | C4 | semidirect |
| 36. #13095495 | C2×C4 | semidirect |
| 37. #13095494 | C2×C4 | semidirect |
| 39. C8×D97 | C2×C4 | semidirect |
| 49. C2×C8×C97 | C2×C4 | semidirect |
| 94. C97 | #2913 | semidirect |
| 102. C2×#107 | D97 | semidirect |
| 136. C2×C8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690816 | 2 |
| #20261216 | 2 |
| #20260776 | 2 |
| #20260775 | 2 |
| #20260773 | 2 |
| #20260772 | 2 |
| #107×D97 | 2 |
| C2×#107×C97 | 2 |
| #2913 | 97 |