Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
578 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C107 | #120 |
| commutator | C42 | C22×C4×C107 |
| Frattini, cosocle | C2×C42 | C23×C107 |
| prime radical | C22×D4×C107 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C107×#1993 | C2 | semidirect |
| 5. C107×#1295 | C2 | semidirect |
| 11. #497×C107 | C4 | semidirect |
| 36. C4⋊Q8×C107 | C2×C4 | semidirect |
| 52. #97×C107 | C2×C4 | semidirect |
| 155. #9003 | C107 | direct (N × H) |
| 164. #1993 | C2×C107 | semidirect |
| 166. #1295 | C2×C107 | semidirect |
| 167. C107 | #9003 | direct (N × H) |
| 173. #497 | C4×C107 | semidirect |
| 198. C4⋊Q8 | C2×C4×C107 | semidirect |
| 214. #97 | C2×C4×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#497×C107 | 2 |
| C107×#2379 | 2 |
| C107×#1993 | 2 |
| C2×#329×C107 | 2 |
| C107×#1295 | 2 |
| #9003 | 107 |