Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#15690749 | C2 | semidirect |
| 2. C2×C16×D97 | C2 | semidirect |
| 4. C4⋊#13095486 | C2 | semidirect |
| 5. #20260514 | C2 | semidirect |
| 6. #20260514 | C2 | semidirect |
| 7. #346×C97 | C2 | semidirect |
| 39. C16×C97 | D4 | semidirect |
| 63. C2×D97 | M32 | semidirect |
| 76. C97 | #2168 | semidirect |
| 83. #346 | D97 | semidirect |
| 115. C16 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690749 | 2 |
| C2×C16×D97 | 2 |
| C8×D388 | 2 |
| C4⋊#13095486 | 2 |
| #20260514 | 2 |
| #346×C97 | 2 |
| #2168 | 97 |