Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20261145 | C2 | semidirect |
| 4. #20261144 | C2 | semidirect |
| 5. #20261141 | C2 | semidirect |
| 6. #20261139 | C2 | semidirect |
| 7. #20261132 | C2 | semidirect |
| 11. #501×C97 | C2 | semidirect |
| 52. #13095494 | Q8 | semidirect |
| 102. C8×C97 | C2×Q8 | semidirect |
| 103. #11715895 | C2×Q8 | semidirect |
| 125. C97 | #3165 | semidirect |
| 131. #501 | D97 | semidirect |
| 228. C8 | Q8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261291 | 2 |
| C4⋊Q8×D97 | 2 |
| #20261145 | 2 |
| #20261144 | 2 |
| #20261141 | 2 |
| #20261139 | 2 |
| #20261132 | 2 |
| #20260776 | 2 |
| #20260774 | 2 |
| #20260687 | 2 |
| #501×C97 | 2 |
| #3165 | 97 |