Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
276 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #20260788 | C2 | semidirect |
| 3. #20260467 | C2 | semidirect |
| 4. #20260464 | C2 | semidirect |
| 5. C2×C4×C8×C97 | C2 | semidirect |
| 24. #13095511 | C8 | semidirect |
| 68. D388 | C2×C8 | semidirect |
| 73. Dic194 | C2×C8 | semidirect |
| 99. C97 | #1476 | semidirect |
| 102. C2×C4×C8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095511 | 2 |
| #20260788 | 2 |
| #20260467 | 2 |
| #20260464 | 2 |
| C2×C4×C8×C97 | 2 |
| #1476 | 97 |