Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
772 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 212 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×C139 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C139 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ C22×C4×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #585×C139 | C2 | semidirect |
| 2. #535×C139 | C2 | semidirect |
| 3. B(4,𝔽2)×C139 | C2 | semidirect |
| 4. #410×C139 | C2 | semidirect |
| 10. C22×D4×C139 | C22 | semidirect |
| 14. #120×C139 | C22 | semidirect |
| 15. #117×C139 | C22 | semidirect |
| 16. #99×C139 | C22 | semidirect |
| 24. C2×Q8×C139 | D4 | semidirect |
| 30. C2×D4×C139 | D4 | semidirect |
| 33. C22×C4×C139 | D4 | semidirect |
| 74. C139 | #3027 | direct (N × H) |
| 75. #3027 | C139 | direct (N × H) |
| 76. #585 | C2×C139 | semidirect |
| 77. #535 | C2×C139 | semidirect |
| 78. B(4,𝔽2) | C2×C139 | semidirect |
| 79. #410 | C2×C139 | semidirect |
| 85. C22×D4 | C22×C139 | semidirect |
| 89. #120 | C22×C139 | semidirect |
| 90. #117 | C22×C139 | semidirect |
| 91. #99 | C22×C139 | semidirect |
| 99. C2×Q8 | D4×C139 | semidirect |
| 105. C2×D4 | D4×C139 | semidirect |
| 108. C22×C4 | D4×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #585×C139 | 2 |
| #535×C139 | 2 |
| B(4,𝔽2)×C139 | 2 |
| #410×C139 | 2 |
| #3027 | 139 |