Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#15690843 | C2 | semidirect |
| 2. C2×#15690840 | C2 | semidirect |
| 4. C2×#15690738 | C2 | semidirect |
| 5. #20260641 | C2 | semidirect |
| 6. #20260503 | C2 | semidirect |
| 7. C2×#104×C97 | C2 | semidirect |
| 41. C2×Dic194 | D4 | semidirect |
| 53. #13095495 | D4 | semidirect |
| 71. M16×C97 | D4 | semidirect |
| 145. C97 | #2007 | semidirect |
| 150. C2×#104 | D97 | semidirect |
| 210. M16 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690843 | 2 |
| C2×#15690840 | 2 |
| #20261313 | 2 |
| C2×#15690738 | 2 |
| #20260641 | 2 |
| #20260503 | 2 |
| C2×#104×C97 | 2 |
| #2007 | 97 |