Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
162 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 69 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×#15690749 | C2 | semidirect |
| 4. #20260553 | C2 | semidirect |
| 5. #20260514 | C2 | semidirect |
| 6. C16×Dic97 | C2 | semidirect |
| 7. C22⋊C16×C97 | C2 | semidirect |
| 32. #13095486 | D4 | semidirect |
| 69. Dic97 | M32 | semidirect |
| 76. C97 | #2169 | semidirect |
| 82. C22⋊C16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690750 | 2 |
| C2×#15690749 | 2 |
| C8×C22⋊D97 | 2 |
| #20260553 | 2 |
| #20260514 | 2 |
| C16×Dic97 | 2 |
| C22⋊C16×C97 | 2 |
| #2169 | 97 |