Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
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×Dic157 | C2 | semidirect |
| 2. #23757290 | C2 | semidirect |
| 3. C2×#19097698 | C2 | semidirect |
| 4. #23757247 | C2 | semidirect |
| 5. #23757045 | C2 | semidirect |
| 6. #23757034 | C2 | semidirect |
| 24. #137×C157 | C4 | semidirect |
| 26. AGL(1,ℤ/8)×C157 | C4 | semidirect |
| 54. C2×Q8×C157 | C2×C4 | semidirect |
| 58. C2×D4×C157 | C2×C4 | semidirect |
| 68. M16×C157 | C2×C4 | semidirect |
| 129. C157 | #1906 | semidirect |
| 141. #137 | Dic157 | semidirect |
| 143. AGL(1,ℤ/8) | Dic157 | semidirect |
| 167. C2×Q8 | C2×Dic157 | semidirect |
| 171. C2×D4 | C2×Dic157 | semidirect |
| 185. M16 | C2×Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic157 | 2 |
| #23757290 | 2 |
| C2×#19097698 | 2 |
| #23757247 | 2 |
| #23757045 | 2 |
| #23757034 | 2 |
| #575×C157 | 2 |
| #1906 | 157 |