Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. #20260560 | C2 | semidirect |
| 4. #20260539 | C2 | semidirect |
| 6. #20260511 | C2 | semidirect |
| 7. C4×Q16×C97 | C2 | semidirect |
| 10. #15690753 | C4 | semidirect |
| 27. #13095486 | C2×C4 | semidirect |
| 30. Q16×C97 | C2×C4 | semidirect |
| 68. C97 | #2175 | semidirect |
| 70. C4×Q16 | D97 | semidirect |
| 92. Q16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690753 | 2 |
| C4×D776 | 2 |
| #20260560 | 2 |
| #20260539 | 2 |
| #20260535 | 2 |
| #20260511 | 2 |
| C4×Q16×C97 | 2 |
| #2175 | 97 |