Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 1. #41×Dic97 | C2 | semidirect |
| 2. #20260752 | C2 | semidirect |
| 3. C2×#15690737 | C2 | semidirect |
| 4. #20260709 | C2 | semidirect |
| 5. #20260507 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 24. #137×C97 | C4 | semidirect |
| 26. AGL(1,ℤ/8)×C97 | C4 | semidirect |
| 54. C2×Q8×C97 | C2×C4 | semidirect |
| 58. C2×D4×C97 | C2×C4 | semidirect |
| 68. M16×C97 | C2×C4 | semidirect |
| 130. C97 | #1906 | semidirect |
| 141. #137 | Dic97 | semidirect |
| 143. AGL(1,ℤ/8) | Dic97 | semidirect |
| 167. C2×Q8 | C2×Dic97 | semidirect |
| 171. C2×D4 | C2×Dic97 | semidirect |
| 185. M16 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic97 | 2 |
| #20260752 | 2 |
| C2×#15690737 | 2 |
| #20260709 | 2 |
| #20260507 | 2 |
| #20260496 | 2 |
| #575×C97 | 2 |
| #1906 | 97 |