Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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. #20261537 | C2 | semidirect |
| 2. #20261170 | C2 | semidirect |
| 3. C2×D1552 | C2 | semidirect |
| 4. #20261006 | C2 | semidirect |
| 5. #20260547 | C2 | semidirect |
| 6. #20260518 | C2 | semidirect |
| 7. #359×C97 | C2 | semidirect |
| 14. C2×D776 | C22 | semidirect |
| 20. #15690750 | C22 | semidirect |
| 23. C2×C16×C97 | C22 | semidirect |
| 24. #108×C97 | C22 | semidirect |
| 94. C97 | #2192 | semidirect |
| 100. #359 | D97 | semidirect |
| 116. C2×C16 | C2×D97 | semidirect |
| 117. #108 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261537 | 2 |
| #20261170 | 2 |
| C2×D1552 | 2 |
| #20261006 | 2 |
| #20260547 | 2 |
| #20260518 | 2 |
| #359×C97 | 2 |
| #2192 | 97 |