Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15690750 | C2 | semidirect |
| 2. C2×#15690744 | C2 | semidirect |
| 3. #20260539 | C2 | semidirect |
| 4. #20260536 | C2 | semidirect |
| 13. #135×C97 | C4 | semidirect |
| 30. Q16×C97 | C2×C4 | semidirect |
| 33. D8×C97 | C2×C4 | semidirect |
| 74. C97 | #2139 | semidirect |
| 82. #135 | Dic97 | semidirect |
| 101. Q16 | C2×Dic97 | semidirect |
| 104. D8 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690750 | 2 |
| C2×#15690744 | 2 |
| #20260539 | 2 |
| #20260536 | 2 |
| C2×#135×C97 | 2 |
| #2139 | 97 |