Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q16×D97 | C2 | semidirect |
| 2. C2×#15690755 | C2 | semidirect |
| 3. C2×#15690753 | C2 | semidirect |
| 5. #20260538 | C2 | semidirect |
| 6. #20260514 | C2 | semidirect |
| 7. #358×C97 | C2 | semidirect |
| 32. Dic388 | D4 | semidirect |
| 43. Q16×C97 | D4 | semidirect |
| 74. C2×D97 | SD32 | semidirect |
| 87. C97 | #2185 | semidirect |
| 93. #358 | D97 | semidirect |
| 123. Q16 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D97 | 2 |
| C2×#15690755 | 2 |
| C2×#15690753 | 2 |
| #20260972 | 2 |
| #20260538 | 2 |
| #20260514 | 2 |
| #358×C97 | 2 |
| #2185 | 97 |