Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×#21439985 | C2 | semidirect |
| 2. C2×#21439956 | C2 | semidirect |
| 3. C2×#21439887 | C2 | semidirect |
| 4. #29504776 | C2 | semidirect |
| 5. C2×#21439877 | C2 | semidirect |
| 6. #29504531 | C2 | semidirect |
| 7. #535×C239 | C2 | semidirect |
| 35. C2×D956 | D4 | semidirect |
| 44. #16838532 | D4 | semidirect |
| 48. C4×Dic239 | D4 | semidirect |
| 54. C2×Q8×C239 | D4 | semidirect |
| 63. C2×D4×C239 | D4 | semidirect |
| 66. C4⋊C4×C239 | D4 | semidirect |
| 138. C239 | #2002 | semidirect |
| 141. #535 | D239 | semidirect |
| 174. C2×Q8 | C22⋊D239 | semidirect |
| 191. C2×D4 | C22⋊D239 | semidirect |
| 203. C4⋊C4 | C22⋊D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439985 | 2 |
| C2×#21439956 | 2 |
| C2×#21439887 | 2 |
| #29504776 | 2 |
| C2×#21439877 | 2 |
| #29504531 | 2 |
| #535×C239 | 2 |
| #2002 | 239 |