Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15690734 | C2 | semidirect |
| 4. #20260498 | C2 | semidirect |
| 5. C22×Q16×C97 | C2 | semidirect |
| 48. C22×D97 | Q16 | semidirect |
| 93. C97 | #2001 | semidirect |
| 94. C22×Q16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690786 | 2 |
| C2×#15690734 | 2 |
| C2×#15690722 | 2 |
| #20260498 | 2 |
| C22×Q16×C97 | 2 |
| #2001 | 97 |