Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 2. C2×#16812753 | C2 | semidirect |
| 4. (C2×#89137)⋊C8 | C2 | semidirect |
| 7. C2×D109⋊C8 | C4 | semidirect |
| 10. C22×#11724786 | C4 | semidirect |
| 17. C22⋊#11724784 | C4 | semidirect |
| 18. #16812611 | C4 | semidirect |
| 19. C22⋊C8×C109 | C4 | semidirect |
| 66. #11724786 | C22⋊C4 | semidirect |
| 71. C22×C109 | #97 | semidirect |
| 76. C2×D109 | #97 | semidirect |
| 93. C109 | #1752 | semidirect |
| 110. C22⋊C8 | #89137 | semidirect |
| 171. C22 | #16812753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D109⋊C8 | 2 |
| C2×#16812753 | 2 |
| C4×C22⋊#89137 | 2 |
| (C2×#89137)⋊C8 | 2 |
| C22⋊C8×D109 | 2 |
| #1752 | 109 |