Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20261143 | C2 | semidirect |
| 3. #20261141 | C2 | semidirect |
| 4. #20261139 | C2 | semidirect |
| 5. #20261137 | C2 | semidirect |
| 6. #20261136 | C2 | semidirect |
| 11. #500×C97 | C2 | semidirect |
| 42. #13095494 | Q8 | semidirect |
| 45. C8×D97 | Q8 | semidirect |
| 108. C97 | #3164 | semidirect |
| 113. #500 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261362 | 2 |
| #20261143 | 2 |
| #20261141 | 2 |
| #20261139 | 2 |
| #20261137 | 2 |
| #20261136 | 2 |
| #20260776 | 2 |
| #20260772 | 2 |
| #107×D97 | 2 |
| #20260689 | 2 |
| #500×C97 | 2 |
| #3164 | 97 |