Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
258 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 74 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. C107×#1376 | C2 | semidirect |
| 3. C107×#1273 | C2 | semidirect |
| 14. C2×Q16×C107 | C8 | semidirect |
| 16. C2×D8×C107 | C8 | semidirect |
| 106. #7114 | C107 | direct (N × H) |
| 114. #1376 | C2×C107 | semidirect |
| 115. #1273 | C2×C107 | semidirect |
| 116. C107 | #7114 | direct (N × H) |
| 127. C2×Q16 | C8×C107 | semidirect |
| 129. C2×D8 | C8×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#1974 | 2 |
| C107×#1376 | 2 |
| C107×#1273 | 2 |
| #7114 | 107 |