Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
652 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 182 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×Q8×#89137 | C2 | semidirect |
| 3. (C2×#89137)⋊Q8 | C2 | semidirect |
| 5. #20295976 | C2 | semidirect |
| 6. #20295970 | C2 | semidirect |
| 7. C22⋊C4×#89137 | C2 | semidirect |
| 8. C42×#89137 | C2 | semidirect |
| 27. #16812688 | C4 | semidirect |
| 28. #16812687 | C4 | semidirect |
| 29. #16812686 | C4 | semidirect |
| 30. #16812685 | C4 | semidirect |
| 33. #124×C109 | C4 | semidirect |
| 52. C2×Dic218 | C2×C4 | semidirect |
| 53. C2×Dic218 | C2×C4 | semidirect |
| 63. C22⋊Dic109 | C2×C4 | semidirect |
| 64. #13182006 | C2×C4 | semidirect |
| 65. #13182006 | C2×C4 | semidirect |
| 66. C4×Dic109 | C2×C4 | semidirect |
| 67. C4×Dic109 | C2×C4 | semidirect |
| 68. C2×Q8×C109 | C2×C4 | semidirect |
| 70. C22⋊C4×C109 | C2×C4 | semidirect |
| 71. C42×C109 | C2×C4 | semidirect |
| 125. #89137 | #124 | direct (N × H) |
| 140. C109 | C4×#124 | semidirect |
| 157. #124 | #89137 | direct (N × H) |
| 179. C2×Q8 | C2×#89137 | semidirect |
| 203. C22⋊C4 | C2×#89137 | semidirect |
| 211. C42 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#89137 | 2 |
| C2×D4×#89137 | 2 |
| (C2×#89137)⋊Q8 | 2 |
| #20295978 | 2 |
| #20295976 | 2 |
| #20295970 | 2 |
| C22⋊C4×#89137 | 2 |
| C42×#89137 | 2 |
| #124×D109 | 2 |
| C4×#124 | 109 |