Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20260814 | C2 | semidirect |
| 3. #20260485 | C2 | semidirect |
| 4. D4⋊#11715895 | C2 | semidirect |
| 5. #20260462 | C2 | semidirect |
| 6. #20260457 | C2 | semidirect |
| 7. #436×C97 | C2 | semidirect |
| 63. #11715895 | M16 | semidirect |
| 84. C97 | #1594 | semidirect |
| 87. #436 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095496 | 2 |
| #20260814 | 2 |
| #20260485 | 2 |
| D4⋊#11715895 | 2 |
| #20260462 | 2 |
| #20260457 | 2 |
| #436×C97 | 2 |
| #1594 | 97 |