Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
272 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 13. #16812766 | C4 | semidirect |
| 14. C4⋊#11724786 | C4 | semidirect |
| 21. #16812610 | C4 | semidirect |
| 22. #16812609 | C4 | semidirect |
| 23. #16812609 | C4 | semidirect |
| 24. #97×C109 | C4 | semidirect |
| 75. C8×C109 | C4⋊C4 | semidirect |
| 77. #11724784 | C4⋊C4 | semidirect |
| 99. C109 | #1771 | semidirect |
| 121. #97 | #89137 | semidirect |
| 176. C8 | C4⋊#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊(C4⋊C8) | 2 |
| C2×#16812753 | 2 |
| C2×C8×#89137 | 2 |
| C4×C4⋊#89137 | 2 |
| (C2×#89137)⋊C8 | 2 |
| #97×D109 | 2 |
| #1771 | 109 |