Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
460 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 460 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. #20260782 | C2 | direct (N × H) |
| 4. C2×#15690746 | C2 | semidirect |
| 5. C2×#15690745 | C2 | semidirect |
| 6. C2×#108×C97 | C2 | semidirect |
| 17. #15690746 | C22 | semidirect |
| 18. #15690745 | C22 | semidirect |
| 21. #108×C97 | C22 | semidirect |
| 83. C2×C97 | #430 | semidirect |
| 87. C97 | C2×#430 | semidirect |
| 93. C2×#108 | D97 | semidirect |
| 108. #108 | C2×D97 | semidirect |
| 171. C2 | #20260782 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095494 | 2 |
| C2×M16×D97 | 2 |
| #20260782 | 2 |
| C2×#15690746 | 2 |
| C2×#15690745 | 2 |
| C2×#108×C97 | 2 |
| C2×#430 | 97 |