Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
294 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 294 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.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C107 | #2184 |
| commutator, Frattini, cosocle | C2×C16 | C23×C107 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C107 ◁ C2×C4×C107 ◁ C22×C8×C107 ◁ C2×M32×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C107×#3414 | C2 | semidirect |
| 2. C107×#2263 | C2 | semidirect |
| 3. C107×#2218 | C2 | semidirect |
| 4. C107×#1418 | C2 | semidirect |
| 5. C107×#1400 | C2 | semidirect |
| 11. C2×D16×C107 | C22 | semidirect |
| 16. M64×C107 | C22 | semidirect |
| 17. #367×C107 | C22 | semidirect |
| 31. Q32×C107 | D4 | semidirect |
| 36. D16×C107 | D4 | semidirect |
| 106. #13667 | C107 | direct (N × H) |
| 112. #3414 | C2×C107 | semidirect |
| 113. #2263 | C2×C107 | semidirect |
| 114. #2218 | C2×C107 | semidirect |
| 115. #1418 | C2×C107 | semidirect |
| 116. #1400 | C2×C107 | semidirect |
| 117. C107 | #13667 | direct (N × H) |
| 123. C2×D16 | C22×C107 | semidirect |
| 128. M64 | C22×C107 | semidirect |
| 129. #367 | C22×C107 | semidirect |
| 143. Q32 | D4×C107 | semidirect |
| 148. D16 | D4×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#3414 | 2 |
| C107×#2263 | 2 |
| C107×#2218 | 2 |
| C107×#1418 | 2 |
| C107×#1400 | 2 |
| #13667 | 107 |