Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. C2×#15690749 | C2 | semidirect |
| 3. M32×D97 | C2 | semidirect |
| 4. #20260520 | C2 | semidirect |
| 5. #20260519 | C2 | semidirect |
| 6. #20260518 | C2 | semidirect |
| 7. #350×C97 | C2 | semidirect |
| 18. #15690750 | C22 | semidirect |
| 22. C2×#13095486 | C22 | semidirect |
| 25. M32×C97 | C22 | semidirect |
| 26. C2×C16×C97 | C22 | semidirect |
| 109. C97 | #2117 | semidirect |
| 116. #350 | D97 | semidirect |
| 132. M32 | C2×D97 | semidirect |
| 135. C2×C16 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D97 | 2 |
| C2×#15690749 | 2 |
| M32×D97 | 2 |
| #20260520 | 2 |
| #20260519 | 2 |
| #20260518 | 2 |
| #350×C97 | 2 |
| #2117 | 97 |