Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 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×C109 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C23×C109 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C22×C4×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #575×C109 | C2 | semidirect |
| 2. C2×AGL(1,ℤ/8)×C109 | C2 | semidirect |
| 3. #535×C109 | C2 | semidirect |
| 4. #421×C109 | C2 | semidirect |
| 5. #418×C109 | C2 | semidirect |
| 6. #410×C109 | C2 | semidirect |
| 7. #344×C109 | C2 | semidirect |
| 41. C2×Q8×C109 | D4 | semidirect |
| 52. C2×D4×C109 | D4 | semidirect |
| 65. M16×C109 | D4 | semidirect |
| 67. C2×C8×C109 | D4 | semidirect |
| 142. #2008 | C109 | direct (N × H) |
| 143. C109 | #2008 | direct (N × H) |
| 144. #575 | C2×C109 | semidirect |
| 145. C2×AGL(1,ℤ/8) | C2×C109 | semidirect |
| 146. #535 | C2×C109 | semidirect |
| 147. #421 | C2×C109 | semidirect |
| 148. #418 | C2×C109 | semidirect |
| 149. #410 | C2×C109 | semidirect |
| 150. #344 | C2×C109 | semidirect |
| 184. C2×Q8 | D4×C109 | semidirect |
| 195. C2×D4 | D4×C109 | semidirect |
| 208. M16 | D4×C109 | semidirect |
| 210. C2×C8 | D4×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #575×C109 | 2 |
| C2×AGL(1,ℤ/8)×C109 | 2 |
| #535×C109 | 2 |
| #421×C109 | 2 |
| #418×C109 | 2 |
| #410×C109 | 2 |
| #344×C109 | 2 |
| #2008 | 109 |