Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
564 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 232 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×C109 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C109 |
| prime radical | C22×D4×C109 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C2×C42×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q16×C109 | C2 | semidirect |
| 3. C2×C4⋊Q8×C109 | C2 | semidirect |
| 5. #497×C109 | C2 | direct (N × H) |
| 6. C2×#97×C109 | C2 | semidirect |
| 11. C2×Q16×C109 | C22 | semidirect |
| 16. C4⋊Q8×C109 | C22 | semidirect |
| 22. #97×C109 | C22 | semidirect |
| 79. C2×C109 | #497 | direct (N × H) |
| 82. C2×#497 | C109 | direct (N × H) |
| 83. C109 | C2×#497 | direct (N × H) |
| 84. C22×Q16 | C2×C109 | semidirect |
| 86. C2×C4⋊Q8 | C2×C109 | semidirect |
| 88. #497 | C2×C109 | direct (N × H) |
| 89. C2×#97 | C2×C109 | semidirect |
| 94. C2×Q16 | C22×C109 | semidirect |
| 99. C4⋊Q8 | C22×C109 | semidirect |
| 105. #97 | C22×C109 | semidirect |
| 162. C2 | #497×C109 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C109 | 2 |
| C22×SD16×C109 | 2 |
| C2×C4⋊Q8×C109 | 2 |
| C2×#124×C109 | 2 |
| #497×C109 | 2 |
| C2×#97×C109 | 2 |
| C2×#497 | 109 |